1MA 03. NOMBRES COMPLEXOS/1MA.03.1 Unitat i, EqG2 en ℂ 1MA.03.1.10DT Eq 2n grau ax^2+c Equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«mrow»«msup mathcolor=¨#FFFFC3¨»«mi mathcolor=¨#FFFFC3¨»ax«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#FFFFC3¨»+«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#FFFFC3¨»c«/mi»«mo mathcolor=¨#FFFFC3¨»§#160;«/mo»«mo mathcolor=¨#FFFFC3¨»=«/mo»«mo mathcolor=¨#FFFFC3¨»§#160;«/mo»«mn mathcolor=¨#FFFFC3¨»0«/mn»«mo mathcolor=¨#FFFFC3¨»§#160;«/mo»«mo mathcolor=¨#FFFFC3¨»(«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#FFFFC3¨»a«/mi»«mo mathcolor=¨#FFFFC3¨»§#183;«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#FFFFC3¨»c«/mi»«mo mathcolor=¨#FFFFC3¨»§#62;«/mo»«mn mathcolor=¨#FFFFC3¨»0«/mn»«mo mathcolor=¨#FFFFC3¨»)«/mo»«/mrow»«/mstyle»«/math»en ℂ
Si l'equació és del tipus ax² + c = 0, i a·c>0, aïlla la x:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»ax«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»ax«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«/mrow»«/mstyle»«/math»

Com que -c/a és negatiu, es transforma en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msup mathcolor=¨#FF0000¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»i«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mstyle»«/math»
I les solucions són: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#177;«/mo»«msqrt mathcolor=¨#003300¨»«mfrac»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#177;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«msqrt mathcolor=¨#003300¨»«mfrac»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«/msqrt»«/mrow»«/mstyle»«/math»

La fracció i l'arrel es simplifiquen, si es pot.

]]> 0.0000000 0.0000000 0 1MA.03.1.11Q Eq 2G ax^2+c (enters) Troba les solucions de l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»11«/mn»«/mrow»«/mstyle»«/math» en el conjunt dels complexos.

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mo»-«/mo»«mfrac»«mrow»«mi»i«/mi»«mo»§#183;«/mo»«msqrt»«mn»6«/mn»«/msqrt»«/mrow»«mn»2«/mn»«/mfrac»«mo»,«/mo»«mfrac»«mrow»«mi»i«/mi»«mo»§#183;«/mo»«msqrt»«mn»6«/mn»«/msqrt»«/mrow»«mn»2«/mn»«/mfrac»«/mrow»«/mfenced»«mo»§#160;«/mo»«mo»(«/mo»«mi»c«/mi»«mi»l«/mi»«mi»a«/mi»«mi»u«/mi»«mi»s«/mi»«mo»)«/mo»«/mstyle»«/math» racionalitzada i simplificada.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msup><mi>a1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>s</mi><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mo>-</mo><mi>s</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mfrac><mi>c_1</mi><mi>a_1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mo>-</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><msqrt><mi>i</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_11</mi><mo>=</mo><mi>s</mi><mo>*</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>s</mi><mo>*</mo><mi>c</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>s</mi><mo>*</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>s</mi><mo>*</mo><mi>c</mi><mo>=</mo><mn>0</mn><mo>,</mo><complexes/></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msub><mi>A</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>A</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>,</mo><mn>16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>16</mn><mn>25</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>16</mn><mn>25</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>16</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mo>*</mo><imaginaryi/></mrow><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mn>4</mn><mo>*</mo><imaginaryi/></mrow><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mrow><mn>4</mn><mo>*</mo><imaginaryi/></mrow><mn>5</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>4</mn><mo>*</mo><imaginaryi/></mrow><mn>5</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_rationalized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Aïllo x²: #a_1 x² = #c_1 i divideixo per #a_1: x² = #h .
Com que és negatiu, el transformo en: x² = #i i²
que té dues arrels.

]]> 1MA.03.1.15Q Eq 2G ax^2+c (irracional) Troba les solucions de l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»11«/mn»«/mrow»«/mstyle»«/math» en el conjunt dels complexos.

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mo»-«/mo»«mfrac»«mrow»«mi»i«/mi»«mo»§#183;«/mo»«msqrt»«mn»6«/mn»«/msqrt»«/mrow»«mn»2«/mn»«/mfrac»«mo»,«/mo»«mfrac»«mrow»«mi»i«/mi»«mo»§#183;«/mo»«msqrt»«mn»6«/mn»«/msqrt»«/mrow»«mn»2«/mn»«/mfrac»«/mrow»«/mfenced»«mo»§#160;«/mo»«mo»(«/mo»«mi»c«/mi»«mi»l«/mi»«mi»a«/mi»«mi»u«/mi»«mi»s«/mi»«mo»)«/mo»«/mstyle»«/math» racionalitzada i simplificada.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>s</mi><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mo>-</mo><mi>s</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mfrac><mi>c_1</mi><mi>a_1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mo>-</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi><mo>=</mo><msqrt><mi>i</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_11</mi><mo>=</mo><mi>s</mi><mo>*</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>s</mi><mo>*</mo><mi>c</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>s</mi><mo>*</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>s</mi><mo>*</mo><mi>c</mi><mo>=</mo><mn>0</mn><mo>,</mo><complexes/></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msub><mi>A</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>A</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>j</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><imaginaryi/></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><imaginaryi/></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><imaginaryi/><mo>,</mo><imaginaryi/></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="check_rationalized"/><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Aïllo x²: #a_1 x² = #c_1 i divideixo per #a_1: x² = #h .
Com que és negatiu, el transformo en: x² = #i i²
que té dues arrels.

]]> 1MA.03.1.40DT E2G ax2+bx+c (Δ

Equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«mrow»«msup mathcolor=¨#FFFFC3¨»«mi mathcolor=¨#FFFFC3¨»ax«/mi»«mn»2«/mn»«/msup»«mo mathcolor=¨#FFFFC3¨»+«/mo»«mi mathcolor=¨#FFFFC3¨»bx«/mi»«mo mathcolor=¨#FFFFC3¨»+«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#FFFFC3¨»c«/mi»«mo mathcolor=¨#FFFFC3¨»§#160;«/mo»«mo mathcolor=¨#FFFFC3¨»(«/mo»«mi mathvariant=¨normal¨ mathcolor=¨#FFFFC3¨»§#916;«/mi»«mo mathcolor=¨#FFFFC3¨»§#60;«/mo»«mn mathcolor=¨#FFFFC3¨»0«/mn»«mo mathcolor=¨#FFFFC3¨»)«/mo»«/mrow»«/mstyle»«/math» en ℂ

En el conjunt dels complexos, les equacions de 2n grau es fan igual que en el conjunt dels reals, però si el discriminant és negatiu (Δ=-K), es substitueix per Δ=Ki².
Es calcula primer el discriminant: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#916;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfenced mathcolor=¨#003300¨ open=¨[¨ close=¨]¨»«mrow»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math» = -K
Com que és negatiu, el substitueix per Ki².
Les solucions són «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mi mathvariant=¨bold¨»K«/mi»«msup mathcolor=¨#FF0000¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»i«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#177;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»i«/mi»«msqrt»«mi mathvariant=¨bold¨»K«/mi»«/msqrt»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1MA.03.1.41Q Eq2G (CoefEnters) Troba les solucions de l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»11«/mn»«/mstyle»«/math» en el conjunt dels complexos.

Format de la resposta: {3-2i,3+3i} amb CLAUS

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><msup><mfenced><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>a</mi><mo>*</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup><mo>)</mo><mo><</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mfenced><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>a</mi><mo>*</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><msqrt><mi>g</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mo>(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>*</mo><imaginaryi/><mo>)</mo><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mo>(</mo><mi>b</mi><mo>-</mo><mi>c</mi><mo>*</mo><imaginaryi/><mo>)</mo><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mo>(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>*</mo><imaginaryi/><mo>)</mo><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mo>(</mo><mi>b</mi><mo>-</mo><mi>c</mi><mo>*</mo><imaginaryi/><mo>)</mo><mo>)</mo><mo>=</mo><mn>0</mn><mo>,</mo><complexes/></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><msub><mi>A</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><msub><mi>A</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>z</mi><mo>,</mo><mi>t</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1764</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1764</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_11</mi><mo>,</mo><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>42</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>294</mn><mo>=</mo><mn>0</mn><mo>,</mo><mo>-</mo><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>7</mn><mo>-</mo><mn>7</mn><mo>*</mo><imaginaryi/></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>7</mn><mo>+</mo><mn>7</mn><mo>*</mo><imaginaryi/></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>-</mo><mn>7</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>+</mo><mn>7</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>7</mn><mo>-</mo><mn>7</mn><mo>*</mo><imaginaryi/><mo>,</mo><mn>7</mn><mo>+</mo><mn>7</mn><mo>*</mo><imaginaryi/></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que el discriminant, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#916;«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«/math»#d, és negatiu el transformem en #g * i², que té dues arrels ± #h * i. Això ens permet calcular les dues solucions amb l'expressió:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#177;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»h«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»*«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1MA.03.1.42Q Eq2G (CoefEnters)_2 Troba les solucions de l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»11«/mn»«/mstyle»«/math» en el conjunt dels complexos.

Format de la resposta: {3-2i,3+3i} amb CLAUS

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><msup><mfenced><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>a</mi><mo>*</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup><mo>)</mo><mo><</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mfenced><mrow><mo>-</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>a</mi><mo>*</mo><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mo>-</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><msqrt><mi>g</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_11</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mo>(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>*</mo><imaginaryi/><mo>)</mo><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mo>(</mo><mi>b</mi><mo>-</mo><mi>c</mi><mo>*</mo><imaginaryi/><mo>)</mo><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>a</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mo>(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>*</mo><imaginaryi/><mo>)</mo><mo>)</mo><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mo>(</mo><mi>b</mi><mo>-</mo><mi>c</mi><mo>*</mo><imaginaryi/><mo>)</mo><mo>)</mo><mo>=</mo><mn>0</mn><mo>,</mo><complexes/></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><msub><mi>A</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><msub><mi>A</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>z</mi><mo>,</mo><mi>t</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1764</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1764</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_11</mi><mo>,</mo><mi>b1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>42</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>294</mn><mo>=</mo><mn>0</mn><mo>,</mo><mo>-</mo><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>7</mn><mo>-</mo><mn>7</mn><mo>*</mo><imaginaryi/></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>7</mn><mo>+</mo><mn>7</mn><mo>*</mo><imaginaryi/></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>-</mo><mn>7</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>+</mo><mn>7</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>7</mn><mo>-</mo><mn>7</mn><mo>*</mo><imaginaryi/><mo>,</mo><mn>7</mn><mo>+</mo><mn>7</mn><mo>*</mo><imaginaryi/></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que el discriminant, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#916;«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«/math»#d, és negatiu el transformem en #g * i², que té dues arrels ± #h * i. Això ens permet calcular les dues solucions amb l'expressió:

]]> 1MA.03.1.51Q Eq2G (coefQualssevol) Troba les solucions de l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»11«/mn»«/mrow»«/mstyle»«/math» en el conjunt dels complexos.

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»6«/mn»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«msqrt»«mn»467«/mn»«/msqrt»«mo»§#183;«/mo»«mi»i«/mi»«/mrow»«mn»6«/mn»«/mfrac»«mo»,«/mo»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»6«/mn»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«msqrt»«mn»467«/mn»«/msqrt»«mo»§#183;«/mo»«mi»i«/mi»«/mrow»«mn»6«/mn»«/mfrac»«/mrow»«/mfenced»«/mstyle»«/math» amb claus

]]> 1.0000000 0.5000000 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>40</mn><mo>,</mo><mn>40</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mo>(</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo><</mo><mn>0</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D11</mi><mo> </mo><mo>=</mo><mo> </mo><mo>-</mo><mi>D</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_11</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn><mo>,</mo><complexes/></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msub><mi>A</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>A</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>17</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>17</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>-</mo><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>*</mo><imaginaryi/><mo>,</mo><mn>3</mn><mo>+</mo><mn>2</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>*</mo><imaginaryi/></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic"/><assertion name="syntax_expression"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El discriminant és #D. Com que és negatiu cal emprar el fet que i² = -1 i per tant el discriminant és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»D«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»D«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mstyle»«/math»

]]> 1MA.03.1.52Q Eq2G (coefQualssevol)_2 Troba les solucions de l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»11«/mn»«/mrow»«/mstyle»«/math» en el conjunt dels complexos.

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»6«/mn»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«msqrt»«mn»467«/mn»«/msqrt»«mo»§#183;«/mo»«mi»i«/mi»«/mrow»«mn»6«/mn»«/mfrac»«mo»,«/mo»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»6«/mn»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«msqrt»«mn»467«/mn»«/msqrt»«mo»§#183;«/mo»«mi»i«/mi»«/mrow»«mn»6«/mn»«/mfrac»«/mrow»«/mfenced»«/mstyle»«/math» amb claus

]]> 1MA.03.1.60DT POTÈNCIES DE i Potències de i Com que: i = i; i² = -1; i³ = -i; i⁴ = 1

per calcular les potències de i, cal fer la divisió entera de l'exponent per 4 i fixar-se en el residu r:

Exemple 1: i²⁶. 26:4 → 26 = 4·6 +2 (residu 2):

i²⁶ = (i⁴)⁶ · i² = 1 · i² = -1

Exemple 2: i³⁹: 39 = 4·9 + 3 => i³⁹ = (i⁴)⁹ ·i³ = 1·i³ = -i.

]]> 0.0000000 0.0000000 0 1MA.03.1.61Q Potències i Calcula les següents potències de la unitat imaginària, i:

a. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«/mstyle»«/math»

b. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«/mstyle»«/math»

c. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«/mstyle»«/math»

^{d. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/msup»«/mstyle»«/math»}

]]> 1.0000000 0.3333333 0 0 a. =#sol1b. =#sol2c. =#sol3d. =#sol4]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>400</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>17</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>-</mo><mn>98</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>215</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>b</mi><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r3</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>c</mi><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r4</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>d</mi><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msup><imaginaryi/><mi>a</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><msup><imaginaryi/><mi>b</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><msup><imaginaryi/><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><msup><imaginaryi/><mi>d</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>335</mn><mo>,</mo><mn>352</mn><mo>,</mo><mn>237</mn><mo>,</mo><mn>550</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>,</mo><mi>sol2</mi><mo>,</mo><mi>sol3</mi><mo>,</mo><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><imaginaryi/><mo>,</mo><mn>1</mn><mo>,</mo><imaginaryi/><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>,</mo><mi>r2</mi><mo>,</mo><mi>r3</mi><mo>,</mo><mi>r4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>3</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>4</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que les potències de i es repeteixen,

i^4·q+r = i^4·q · i^r = 1 · i^r

Cal doncs fer la divisió entera de la potència per 4.

El residu de la divisió de #a per 4 és #r1, per això «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»s«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»o«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»l«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«/mrow»«/mstyle»«/math»

]]> El residu de la divisió de #b per 4 és #r2

El residu de la divisió de #c per 4 és #r3

El residu de la divisió de #d per 4 és #r4

]]> 1MA.03.1.62Q Potències i_2 Calcula les següents potències de la unitat imaginària, i:

a. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«/mstyle»«/math»

b. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«/mstyle»«/math»

c. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«/mstyle»«/math»

^{d. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»i«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/msup»«/mstyle»«/math»}

i^4·q+r = i^4·q · i^r = 1 · i^r

Cal doncs fer la divisió entera de la potència per 4.

]]> El residu de la divisió de #b per 4 és #r2

El residu de la divisió de #c per 4 és #r3

El residu de la divisió de #d per 4 és #r4

]]> 1MA 03. NOMBRES COMPLEXOS/1MA.03.2 Nombres complexos 1MA.03.2.10DT FORMA BINOMICA

Forma binòmica

En forma binòmica, un nombre complex s'escriu:

z = a + bi on a és la part real, i b és la part imàginària.

bi és un nombre imaginari pur.

Dos nombres complexos són iguals, si tenen:

les parts reals iguals
les parts imaginàries iguals

]]> 0.0000000 0.0000000 0 1MA.03.2.11Q FBinPartRealImaginària a) Quina és la part real del nombre complex «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math» ?

b) Quina és la seva part imaginària?

b. La part imaginària és i amb el seu coeficient

]]> 1MA.03.2.21Q FBinomcaConjugat Quin és el conjugat del nombre complex «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math» ?

]]> 1.0000000 0.5000000 0 0 #r_22]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>15</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>15</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>norma</mi><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>argument</mi><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mfrac><mrow><mi>p</mi><mo>*</mo><mn>180</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></mrow><pi/></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_22</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>12</mn><mo>+</mo><mn>11</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>265</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.74195</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>+</mo><mn>11</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>-</mo><mn>11</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42.51</mn><mo> </mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>22</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal canviar el signe de la part imaginària.

]]> 1MA.03.2.31Q PartRealIgual Quin és el valor de k si els dos nombres complexos «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»k«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math» són iguals?

Format de la resposta: k=-2

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»k«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«/mstyle»«/math»

]]> 1MA.03.2.32Q PartImaginàriaIgual Quin és el valor de k si els dos nombres complexos «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»k«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»k«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«/mstyle»«/math» són iguals?

Format de la resposta: k=-2

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»k«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«/mrow»«/mstyle»«/math»

]]> 1MA.03.2.41 Igualar dos complexos (k) Quin és el valor de k si els dos nombres complexos

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«msub»«mi mathvariant=¨bold¨»z«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨»i«/mi»«/mtd»«/mtr»«mtr»«mtd»«msub»«mi mathvariant=¨bold¨»z«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mi mathvariant=¨bold¨»k«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

són iguals?

Format de la resposta: -2

k - #m = #b

]]> 1MA.03.2.51 Trobar nombre amb representació Considera la representació següent del nombre complex z:

#G

Quin és aquest nombre complex?
Format de la resposta: 2 + 3i

]]> 1.0000000 0.5000000 0 0 #s

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>z</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>+</mo><mn>7</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>22</mn><mo>,</mo><mn>22</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibuix</mi><mo>:</mo><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T</mi><mo>,</mo><mi>z</mi><mo>,</mo><mo> </mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>10</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi><mo>}</mo></mrow></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibuix</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#s</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un nombre complex z=a+b*i es representa al pla amb un punt anomenat afix de coordenades (a,b).

]]> 1MA.03.2.51 Trobar nombre amb representació Considera la representació següent del nombre complex z:

#G

Quin és aquest nombre complex?
Format de la resposta: 2 + 3i

]]> Un nombre complex z=a+b*i es representa al pla amb un punt anomenat afix de coordenades (a,b).

]]> 1.0000000 0.5000000 0 0 #s

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>20</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>z</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>+</mo><mn>7</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>22</mn><mo>,</mo><mn>22</mn><mo>)</mo><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibuix</mi><mo>:</mo><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T</mi><mo>,</mo><mi>z</mi><mo>,</mo><mo> </mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>10</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi><mo>}</mo></mrow></mfenced><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibuix</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#s</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> 1MA.03.2.61 Triar representació amb nombre Quin és el gràfic que correspon al nombre complex:
z = #a #s #b_1 i ?

]]> Si la part real, #a, és positiva, el nombre està en el 1r o 4t quadrant; si és negativa, el nombre està en el 2n o 3r.
Si la part imaginària, #b, és positiva, el nombre està en el 1r o 2n quadrant; si és negativa, en el 3r o 4t. ]]> 1.0000000 0.5000000 0 true true abc #r_1

]]>

]]> #r_2

]]> #r_3

]]> #r_4

]]> <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo> </mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>b</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_3</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_4</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mo>-</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_3</mi><mo>=</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_4</mi><mo>=</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>a</mi><mo>,</mo><mo>-</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T3</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T4</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T1</mi><mo>,</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mo>-</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T3</mi><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T4</mi><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>a</mi><mo>,</mo><mo>-</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler4</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> 1MA.03.2.61 Triar representació amb nombre Quin és el gràfic que correspon al nombre complex:
z = #a #s #b_1 i ?

]]>

]]> #r_2

]]> #r_3

]]> #r_4

]]> <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo> </mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mfenced close="&verbar;" open="&verbar;"><mi>b</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>s</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></mrow><mrow><mi>s</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_3</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_4</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mo>-</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_3</mi><mo>=</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_4</mi><mo>=</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>a</mi><mo>,</mo><mo>-</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T3</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T4</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T1</mi><mo>,</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mo>-</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T3</mi><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T4</mi><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mi>a</mi><mo>,</mo><mo>-</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler4</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> 1MA 03. NOMBRES COMPLEXOS/1MA.03.3 F.binòmPolarTrigon 1MA.03.3.10 TEORIA: DE F.BINÒMICA A F.POLAR

De forma binòmica a forma polar

El nombre complex z = a+bi es pot escriure en forma polar :

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mrow»«mi mathvariant=¨bold¨»§#945;«/mi»«mo»§#176;«/mo»«/mrow»«/msub»«/mrow»«/mstyle»«/math»

r és el MÒDUL. Es calcula amb: r = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«msqrt mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»a«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mi mathvariant=¨bold¨»b«/mi»«mn»2«/mn»«/msup»«/msqrt»«/mstyle»«/math»
α és l' ARGUMENT. Es calcula amb: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#945;«/mi»«mo mathcolor=¨#003300¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»arc«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»tg«/mi»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«/mrow»«/mstyle»«/math».

Els signes de a i b ens indiquen

en quin quadrant està l'afíx del nombre.

]]> 0.0000000 0.0000000 0 1MA.03.3.11Q Binòmica→Polar: Mòdul Quin és el mòdul del nombre «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«/mrow»«/mstyle»«/math» ?

Format de la resposta: arrel simplificada

]]> 1MA.03.3.12Q Binòmica→Polar: Mòdul(Enters) Quin és el mòdul del nombre «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«/mrow»«/mstyle»«/math»?

Format de la resposta: arrel simplificada

]]> 1MA.03.3.13Q Binòmica→polar: Mòdul(Fraccions) Quin és el mòdul del nombre «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«/mrow»«/mstyle»«/math»?

Format de la resposta: arrel simplificada

]]> 1.0000000 0.5000000 0 0 #r <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>na</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>da</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>nb</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>db</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>na</mi><mo>,</mo><mi>da</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>&and;</mo><mi>mcd</mi><mo>(</mo><mi>nb</mi><mo>,</mo><mi>db</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mi>na</mi><mi>da</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mi>nb</mi><mi>db</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>8</mn><mn>23</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>-</mo><mfrac><mrow><mn>8</mn><mo>*</mo><imaginaryi/></mrow><mn>23</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>4</mn><mo>*</mo><msqrt><mn>565</mn></msqrt></mrow><mn>69</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="check_rationalized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Recordes el teorema de Pitàgores?

]]> 1MA.03.3.15Q Binòmica→Polar: Argument(Enters) Quin és l'argument del nombre «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«/mrow»«/mstyle»«/math»?

Format de la resposta: arrodonida a la unitat.

]]> 1.0000000 0.5000000 0 0 #r <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>arrodoneix</mi><mfenced><mrow><mi>atan</mi><mfenced><mfrac><mfenced close="|" open="|"><mi>b</mi></mfenced><mfenced close="|" open="|"><mi>a</mi></mfenced></mfrac></mfenced><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>r</mi><mo>=</mo><mi>a1</mi></mrow><mrow><mi>r</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>a1</mi></mrow></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>r</mi><mo>=</mo><mn>180</mn><mo>-</mo><mi>a1</mi></mrow><mrow><mi>r</mi><mo>=</mo><mn>180</mn><mo>+</mo><mi>a1</mi></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>+</mo><mn>5</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>135</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Mira el gràfic: #G

]]> 1MA.03.3.16Q Binòmica→Polar: Argument(Fraccions) Quin és l'argument del nombre «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«/mrow»«/mstyle»«/math»?

Format de la resposta: arrodonida a la unitat.

]]> 1.0000000 0.5000000 0 0 #r <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>na</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>da</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>nb</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>db</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>na</mi><mo>,</mo><mi>da</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>&and;</mo><mi>mcd</mi><mo>(</mo><mi>nb</mi><mo>,</mo><mi>db</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mi>na</mi><mi>da</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mi>nb</mi><mi>db</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>arrodoneix</mi><mfenced><mrow><mi>atan</mi><mfenced><mfrac><mfenced close="|" open="|"><mi>b</mi></mfenced><mfenced close="|" open="|"><mi>a</mi></mfenced></mfrac></mfenced><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>r</mi><mo>=</mo><mi>a1</mi></mrow><mrow><mi>r</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>a1</mi></mrow></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>r</mi><mo>=</mo><mn>180</mn><mo>-</mo><mi>a1</mi></mrow><mrow><mi>r</mi><mo>=</mo><mn>180</mn><mo>+</mo><mi>a1</mi></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>23</mn><mn>20</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mn>21</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>23</mn><mn>20</mn></mfrac><mo>+</mo><mfrac><mrow><mn>4</mn><mo>*</mo><imaginaryi/></mrow><mn>21</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>171</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Mira el gràfic: #G

]]> 1MA.03.3.21Q Binòmica→mòdul+argument Quin és el mòdul i l'argument del nombre complex «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»z«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mstyle»«/math» ?

Format de la resposta:
r=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mn»2«/mn»«/msqrt»«/math»
a=30 (arrodonit a la unitat)

]]> 1MA.03.3.22Q BinòmICA→Polar: mòdul+argument Calcula el mòdul i l'argument de z = #z?

Format de les respostes: arrel simplificada i angle arrodonit sense unitats

]]> 1.0000000 0.5000000 0 0 |z|=#mArgument=#r]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>arrodoneix</mi><mfenced><mrow><mi>atan</mi><mfenced><mfrac><mfenced close="|" open="|"><mi>b</mi></mfenced><mfenced close="|" open="|"><mi>a</mi></mfenced></mfrac></mfenced><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>r</mi><mo>=</mo><mi>a1</mi></mrow><mrow><mi>r</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>a1</mi></mrow></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>r</mi><mo>=</mo><mn>180</mn><mo>-</mo><mi>a1</mi></mrow><mrow><mi>r</mi><mo>=</mo><mn>180</mn><mo>+</mo><mi>a1</mi></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>-</mo><mn>9</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>246</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>97</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>|</mo><mi>z</mi><mo>|</mo><mo>=</mo><mo>#</mo><mi>m</mi><mspace linebreak="newline"/><mi>A</mi><mi>r</mi><mi>g</mi><mi>u</mi><mi>m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> El mòdul es calcula amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨|¨ close=¨|¨»«mi mathvariant=¨bold¨»z«/mi»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mstyle»«/math»

Mira el gràfic: #G

Situa l'angle i calcula l'arc tangent de b/a

]]> 1MA.03.3.30DT Forma Trigonomètrica

Forma trigonomètrica

El nombre complex z = a+bi es pot escriure en forma trigonomètrica:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mrow»«mi mathvariant=¨bold¨»§#945;«/mi»«mo»§#176;«/mo»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»cos§#945;«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»i«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»sin§#945;«/mi»«/mrow»«/mfenced»«/mstyle»«/math»

Si r és el MÒDUL i α és l' ARGUMENT

]]> 0.0000000 0.0000000 0 1MA.03.3.50DT F. POLAR A F.BINÒMICA

Conversió de forma polar a binòmica

El nombre complex «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mrow»«mi mathvariant=¨bold¨»§#945;«/mi»«mo»§#176;«/mo»«/mrow»«/msub»«/mrow»«/mstyle»«/math», s'escriu,

en FORMA BINÒMICA,

(utilitzant la forma trigonomètrica): «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»cos§#945;«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»+«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathcolor=¨#003300¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sin§#945;«/mi»«mo mathcolor=¨#003300¨»)«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»cos§#945;«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»+«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sin§#945;«/mi»«mo mathcolor=¨#003300¨»)«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«/mrow»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1MA.03.3.51Q Polar→Binòmica Quin és, en forma binòmica, el nombre complex que té per mòdul #m i per argument #r?

Format de la resposta: z=a+bi (coeficients enters).

]]> 1.0000000 0.5000000 0 0 #s <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>arrodoneix</mi><mfenced><mrow><mi>atan</mi><mfenced><mfrac><mfenced close="|" open="|"><mi>b</mi></mfenced><mfenced close="|" open="|"><mi>a</mi></mfenced></mfrac></mfenced><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>r</mi><mo>=</mo><mi>a1</mi></mrow><mrow><mi>r</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>a1</mi></mrow></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>r</mi><mo>=</mo><mn>180</mn><mo>-</mo><mi>a1</mi></mrow><mrow><mi>r</mi><mo>=</mo><mn>180</mn><mo>+</mo><mi>a1</mi></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>z</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>29</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>248</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>-</mo><mn>5</mn><mo>*</mo><imaginaryi/></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Mira el gràfic: #G

]]> 1MA.03.3.52Q Polar→Binòmica_2 Quin és, en forma binòmica, el nombre complex que té per mòdul #m i per argument #r?

Format de la resposta: z=a+bi (coeficients enters).

]]> 1.0000000 0.5000000 0 0 #s <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>arrodoneix</mi><mfenced><mrow><mi>atan</mi><mfenced><mfrac><mfenced close="|" open="|"><mi>b</mi></mfenced><mfenced close="|" open="|"><mi>a</mi></mfenced></mfrac></mfenced><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>></mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>r</mi><mo>=</mo><mi>a1</mi></mrow><mrow><mi>r</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>a1</mi></mrow></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>b</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>r</mi><mo>=</mo><mn>180</mn><mo>-</mo><mi>a1</mi></mrow><mrow><mi>r</mi><mo>=</mo><mn>180</mn><mo>+</mo><mi>a1</mi></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>z</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>29</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>248</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>-</mo><mn>5</mn><mo>*</mo><imaginaryi/></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#s</correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Mira el gràfic: #G

]]> 1MA.03.3.61Q Polar→Binòmica Escriu en forma binòmica, el nombre «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«/math»

Format de la resposta: z=a+bi (coeficients enters).

Dedueix a = r·cosa

b = r· sina

]]> 1MA.03.3.62Q Polar→Binòmica_2 Escriu en forma binòmica, el nombre «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«/math»

Format de la resposta: z=a+bi (coeficients enters).

Dedueix a = r·cosa

b = r· sina

]]> 1MA 03. NOMBRES COMPLEXOS/1MA.03.4 Operar F. Binòmica 1MA.03.4.10DT OPERACIONS (F.BINÒMICA)

Operacions en forma binòmica

ADDICIÓ:
(a+bi) + (c+di) = (a+c) + (b+d)i

La part real de la suma és la suma de les parts reals; la part imaginària de la suma és la suma de les parts imaginàries.

SUBTRACCIÓ:
(a+bi) - (c+di) = (a-c) + (b-d)i

La part real de la diferència és la diferència de les parts reals; la part imaginària de la diferència és la diferència de les parts imaginàries.

MULTIPLICACIÓ:
(a+bi) * (c+di) = ac+adi+bci+bdi²

= (ac-bd) + (ad+bc)i

Multiplico distributivament.Com que i² = -1, bdi² es transforma en -bd.

DIVISIÓ:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»bi«/mi»«/mrow»«mrow»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»di«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mfenced»«mrow»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»bi«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»di«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»di«/mi»«/mrow»«/mfenced»«mfenced»«mrow»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»di«/mi»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«msup»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»bd«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»bc«/mi»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»ad«/mi»«mo mathvariant=¨bold¨»)«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«mrow»«msup»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mfrac»«/mstyle»«/math»

Multiplico i divideixo pel conjugat.Com que i² = -1, -bdi² es transforma en bd.

]]> 0.0000000 0.0000000 0 1MA.03.4.11Q F.Binòmica: suma(Enters) Amb z₁ = #z_1 , z₂ = #z_2, calcula z₁ + z₂

Format de la resposta: 5-3i

]]> 1MA.03.4.12Q F.Binòmica: suma(Fraccions) Amb z₁ = #z_1 , z₂ = #z_2, calcula z₁ + z₂

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»2«/mn»«mn»3«/mn»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mn»3«/mn»«mo»§#183;«/mo»«mi»i«/mi»«/mrow»«mn»4«/mn»«/mfrac»«/math»(fraccions simplificades)

]]> 1.0000000 0.5000000 0 0 #c_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>na1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>da1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>nb1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>db1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>na1</mi><mo>,</mo><mi>da1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>&and;</mo><mi>mcd</mi><mo>(</mo><mi>nb1</mi><mo>,</mo><mi>db1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mfrac><mi>na1</mi><mi>da1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mfrac><mi>nb1</mi><mi>db1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>na2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>da2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>nb2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>db2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>na2</mi><mo>,</mo><mi>da2</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>&and;</mo><mi>mcd</mi><mo>(</mo><mi>nb2</mi><mo>,</mo><mi>db2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>17</mn><mn>11</mn></mfrac><mo>-</mo><mfrac><mrow><mn>10</mn><mo>*</mo><imaginaryi/></mrow><mn>11</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>23</mn><mn>7</mn></mfrac><mo>+</mo><mfrac><mrow><mn>3</mn><mo>*</mo><imaginaryi/></mrow><mn>14</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>372</mn><mn>77</mn></mfrac><mo>-</mo><mfrac><mrow><mn>107</mn><mo>*</mo><imaginaryi/></mrow><mn>154</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="answer_parameter">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Sumem les parts reals entre elles i les parts imaginàries entre elles.

]]> 1MA.03.4.21Q F.BINÒMICA: resta(enters) Amb z₁ = #z_1 , z₂ = #z_2, calcula z₁ - z₂

Format de la resposta: 5-3i

]]> 1.0000000 0.5000000 0 0 #c_11 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><mi>i_</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi><mo>=</mo><mi>a_2</mi><mo>+</mo><mi>b_2</mi><mo>*</mo><mi>i_</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi><mo>=</mo><mi>z_1</mi><mo>-</mo><mi>z_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>+</mo><mn>8</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>+</mo><mn>4</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>+</mo><mn>12</mn><mo>*</mo><imaginaryi/></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#c_11</correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Restem les parts reals

i restem les parts imaginàries

]]> 1MA.03.4.22Q F.BINÒMICA: resta (fraccions) Amb z₁= #z_1 , z₂ = #z_2, calcula z₁ - z₂

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»2«/mn»«mn»3«/mn»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mn»4«/mn»«mo»§#183;«/mo»«mi»i«/mi»«/mrow»«mn»35«/mn»«/mfrac»«/math»(simplificada)

]]> Restem les parts reals entre elles i les parts imaginàries entre elles.

]]> 1.0000000 0.5000000 0 0 #c_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>na1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>da1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>nb1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>db1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>na1</mi><mo>,</mo><mi>da1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>&and;</mo><mi>mcd</mi><mo>(</mo><mi>nb1</mi><mo>,</mo><mi>db1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mfrac><mi>na1</mi><mi>da1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mfrac><mi>nb1</mi><mi>db1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>na2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>da2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>nb2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>db2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>na2</mi><mo>,</mo><mi>da2</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>&and;</mo><mi>mcd</mi><mo>(</mo><mi>nb2</mi><mo>,</mo><mi>db2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mfrac><mi>na2</mi><mi>da2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mfrac><mi>nb2</mi><mi>db2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>b1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>b2</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi><mo>=</mo><mi>z_1</mi><mo>-</mo><mi>z_2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>15</mn><mn>8</mn></mfrac><mo>-</mo><mfrac><mrow><mn>11</mn><mo>*</mo><imaginaryi/></mrow><mn>6</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>23</mn><mn>25</mn></mfrac><mo>+</mo><mfrac><mrow><mn>17</mn><mo>*</mo><imaginaryi/></mrow><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>559</mn><mn>200</mn></mfrac><mo>-</mo><mfrac><mrow><mn>157</mn><mo>*</mo><imaginaryi/></mrow><mn>30</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="answer_parameter">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1MA.03.4.31Q F.BINÒMICA:Comb. lineal(enters) Amb z₁ = #z_1 , z₂ = #z_2, calcula #p · z₁ + #q · z₂

Format de la resposta: 5-3i

]]> 1.0000000 0.5000000 0 0 #c_11 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><mi>i_</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi><mo>=</mo><mi>a_2</mi><mo>+</mo><mi>b_2</mi><mo>*</mo><mi>i_</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>z_1</mi><mo>+</mo><mi>q</mi><mo>*</mo><mi>z_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>11</mn><mo>,</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>+</mo><mn>4</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>-</mo><mn>3</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>57</mn><mo>-</mo><mn>30</mn><mo>*</mo><imaginaryi/></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#c_11</correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Primer multipliquem els nombres pels factors i després, sumem les parts reals entre elles i les parts imaginàries entre elles.

]]> 1MA.03.4.32Q F.BINÒMICA:comb.lineal(fraccions) Amb z₁ = #z_1 , z₂ = #z_2, calcula #p · z₁ - #q · z₂

Format de la resposta: 5-3i_

]]> Primer multipliquem els nombres pels coeficients i després, sumem les parts reals entre elles i les parts imaginàries entre elles.

]]> 1.0000000 0.5000000 0 0 #c_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>na1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>da1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>nb1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>db1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>na1</mi><mo>,</mo><mi>da1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>&and;</mo><mi>mcd</mi><mo>(</mo><mi>nb1</mi><mo>,</mo><mi>db1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mfrac><mi>na1</mi><mi>da1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mfrac><mi>nb1</mi><mi>db1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>na2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>da2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>nb2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>db2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>na2</mi><mo>,</mo><mi>da2</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>&and;</mo><mi>mcd</mi><mo>(</mo><mi>nb2</mi><mo>,</mo><mi>db2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mfrac><mi>na2</mi><mi>da2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mfrac><mi>nb2</mi><mi>db2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>b1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>b2</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi><mo>=</mo><mi>p</mi><mo>*</mo><mi>z_1</mi><mo>-</mo><mi>q</mi><mo>*</mo><mi>z_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>18</mn><mn>23</mn></mfrac><mo>-</mo><mfrac><mrow><mn>17</mn><mo>*</mo><imaginaryi/></mrow><mn>12</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>25</mn><mn>2</mn></mfrac><mo>-</mo><mfrac><mrow><mn>23</mn><mo>*</mo><imaginaryi/></mrow><mn>8</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>2731</mn><mn>46</mn></mfrac><mo>+</mo><mfrac><mrow><mn>209</mn><mo>*</mo><imaginaryi/></mrow><mn>24</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="answer_parameter">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1MA.03.4.41Q F.BINÒMICA: Multiplicació(enters) Amb z₁ = #z_1 , z₂ = #z_2, multiplica z₁ · z₂

Format de la resposta: 5-3i

]]> 1MA.03.4.42 F.BINÒMICA: Multiplicació(fraccions) Amb z₁ = #z_1 , z₂ = #z_2, multiplica z₁ · z₂

Format de la resposta: 5-3i

]]> 1.0000000 0.5000000 0 0 #c_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>na1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>da1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>nb1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>db1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>na1</mi><mo>,</mo><mi>da1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>&and;</mo><mi>mcd</mi><mo>(</mo><mi>nb1</mi><mo>,</mo><mi>db1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mfrac><mi>na1</mi><mi>da1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mfrac><mi>nb1</mi><mi>db1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>na2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>da2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>nb2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>db2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>na2</mi><mo>,</mo><mi>da2</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>&and;</mo><mi>mcd</mi><mo>(</mo><mi>nb2</mi><mo>,</mo><mi>db2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mfrac><mi>na2</mi><mi>da2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mfrac><mi>nb2</mi><mi>db2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>b1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>b2</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi><mo>=</mo><mi>z_1</mi><mo>*</mo><mi>z_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>a2</mi><mo>-</mo><mi>b1</mi><mo>*</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>b2</mi><mo>+</mo><mi>b1</mi><mo>*</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>10</mn><mn>23</mn></mfrac><mo>-</mo><mfrac><mrow><mn>14</mn><mo>*</mo><imaginaryi/></mrow><mn>15</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>21</mn><mn>22</mn></mfrac><mo>-</mo><mfrac><mrow><mn>16</mn><mo>*</mo><imaginaryi/></mrow><mn>21</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>12821</mn><mn>11385</mn></mfrac><mo>+</mo><mfrac><mrow><mn>14867</mn><mo>*</mo><imaginaryi/></mrow><mn>26565</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>12821</mn><mn>11385</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>14867</mn><mn>26565</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="answer_parameter">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal multiplicar distributivament i substituir i² per -1.
La part real és: (#a1) · (#a2) + (#b1) · (#b2) ·i²
La part imaginària és (#a1) · (#b2) + (#b1) · (#a2)

]]> 1MA.03.4.51Q F.BINÒMICA: divisió(enters) Amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mrow»«/mstyle»«/math» , divideix z₁ / z₂

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»3«/mn»«mn»5«/mn»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mn»7«/mn»«mi»i«/mi»«/mrow»«mn»5«/mn»«/mfrac»«/math»

]]> 1MA.03.4.52Q F.BINÒMICA: divisió(fracció) Divideix: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»z_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»z_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac»«mn»3«/mn»«mn»5«/mn»«/mfrac»«mo»-«/mo»«mfrac»«mrow»«mn»7«/mn»«mi»i«/mi»«/mrow»«mn»5«/mn»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #c_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>na1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>da1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>nb1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>db1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>na1</mi><mo>,</mo><mi>da1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>&and;</mo><mi>mcd</mi><mo>(</mo><mi>nb1</mi><mo>,</mo><mi>db1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mfrac><mi>na1</mi><mi>da1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mfrac><mi>nb1</mi><mi>db1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>na2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>da2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>nb2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>db2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>na2</mi><mo>,</mo><mi>da2</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>&and;</mo><mi>mcd</mi><mo>(</mo><mi>nb2</mi><mo>,</mo><mi>db2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mfrac><mi>na2</mi><mi>da2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mfrac><mi>nb2</mi><mi>db2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>b1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>b2</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi><mo>=</mo><mfrac><mi>z_1</mi><mi>z_2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_1</mi><mo>=</mo><mi>a2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>23</mn><mn>18</mn></mfrac><mo>-</mo><mfrac><imaginaryi/><mn>23</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>5</mn><mn>18</mn></mfrac><mo>-</mo><mfrac><mrow><mn>11</mn><mo>*</mo><imaginaryi/></mrow><mn>12</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>9392</mn><mn>27347</mn></mfrac><mo>+</mo><mfrac><mrow><mn>35274</mn><mo>*</mo><imaginaryi/></mrow><mn>27347</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>5</mn><mn>18</mn></mfrac><mo>+</mo><mfrac><mrow><mn>11</mn><mo>*</mo><imaginaryi/></mrow><mn>12</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Multiplica el numerador i el denominador pel conjugat del denominador, #f_1 i efectua les operacions.

]]> 1MA.03.4.60DT Binomi de Newton

Binomi de Newton (a + bi)ⁿ

Triangle de Pascal:

Desenvolupament del Binomi:

els coeficients són els del triangle de Pascal
a va disminuint de grau des de n fins a 0
bi va augmentant de grau des de 0 fins a n
i = i; i² = -1; i³ = -i; i⁴ = 1

Per exemple: (a + bi)⁴

= 1·a⁴ + 4·a³·(bi) + 6·a²·(bi)² + 4·a·(bi)³ + 1·(bi)⁴

= a⁴+ 4a³bi - 6a²b² - 4ab³i + b⁴

]]> 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0.0000000 0.0000000 0 1MA.03.4.61Q F.BINÒMICA: Newton Coeficients Si calcules (#z1)^#n:

a) Quants termes té el desenvolupament?

b) Quin és valor del #p sumand?

]]> 1.0000000 0.5000000 0 0 a. = #sol1b. =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>r</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mfenced><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mfenced><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>b1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi><mo>=</mo><mo>(</mo><mi>z1</mi><msup><mo>)</mo><mi>n</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mi>g</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><msup><mi>a1</mi><mrow><mi>n</mi><mo>-</mo><mi>g</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><msup><mfenced><mrow><mi>b1</mi><mo>*</mo><imaginaryi/></mrow></mfenced><mi>g</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>c1</mi><mo>*</mo><mi>c2</mi><mo>*</mo><mi>c3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r</mi><mo>=</mo><mn>3</mn></mrow><mrow><mi>p</mi><mo>=</mo><mo>"</mo><mi>tercer</mi><mo>"</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>p</mi><mo>=</mo><mo>"</mo><mi>quart</mi><mo>"</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r</mi><mo>=</mo><mn>5</mn></mrow><mrow><mi>p</mi><mo>=</mo><mo>"</mo><mi>cinquè</mi><mo>"</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>r</mi><mo>=</mo><mn>6</mn></mrow><mrow><mi>p</mi><mo>=</mo><mo>"</mo><mi>sisè</mi><mo>"</mo></mrow><mrow><mi>p</mi><mo>=</mo><mo>"</mo><mi>setè</mi><mo>"</mo></mrow></apply></apply></apply></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>-</mo><mn>3</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>r</mi><mo>,</mo><mi>g</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6554</mn><mo>-</mo><mn>4449</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>,</mo><mi>c3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22680</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>cinquè</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo> </mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="answer_parameter">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> El #p sumand es calcula amb

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«mrow»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»g«/mi»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»g«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»g«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math»

]]> 1MA.03.4.71Q BNewton^3 Amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»= #«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math» , calcula z^#n

Format de la resposta: 2-5i

]]> 1.0000000 0.5000000 0 0 #c_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi><mo>=</mo><mo>(</mo><mi>z_1</mi><msup><mo>)</mo><mi>n</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>,</mo><mi>a_2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>-</mo><mn>2</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>65</mn><mo>-</mo><mn>142</mn><mo>*</mo><imaginaryi/></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #c_11 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Aplico el binomi de Newton.
Els coeficients són 1 3 3 1:
1·(#a_1)³ + 3·(#a_1)²·(#b_1 i) + 3·(#a_1)·(#b_1 i)² + 1·(#b_1 i)³Recorda que i² = - 1 i que i³ = -i

]]> 1MA.03.4.72Q BNewton^4 Amb z= «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math» , calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/msup»«/mstyle»«/math»

Format de la resposta: 2-5i

]]> 1MA.03.4.73Q BNewton^5 Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»z_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/msup»«/mstyle»«/math»

Format de la resposta: 2-5i

]]>

Els coeficients són 1 5 10 10 5 1

]]> 1MA.03.4.81Q BNewton: calcular a Quina és la part real del nombre z = #z1 si (#z1)^#n = #c_11?

Format de la resposta: 2-5*i

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi><mo>=</mo><mo>(</mo><mi>a1</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/><msup><mo>)</mo><mi>n</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>resol</mi><mfenced><mfenced><mrow><msup><mfenced><mi>z1</mi></mfenced><mn>3</mn></msup><mo>=</mo><mi>c_11</mi></mrow></mfenced></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>-</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>52</mn><mo>-</mo><mn>47</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>=</mo><mo>-</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>=</mo><mn>1.134</mn><mo>+</mo><mn>4.9641</mn><mo>*</mo><imaginaryi/></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>=</mo><mn>2.866</mn><mo>-</mo><mn>1.9641</mn><mo>*</mo><imaginaryi/></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="answer_parameter">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La part real del resultat es calcula amb: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mstyle»«/math»

La part imaginària del resultat es calcula amb: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»3«/mn»«/msup»«/mrow»«/mstyle»«/math»

Igualo la part real i la part imaginària amb les de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»c_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«/mrow»«/mstyle»«/math».

Atenció: cal que la part real i la part imaginàries siguin iguals!

]]> 1MA 03. NOMBRES COMPLEXOS/1MA.03.5 Operar F. polar 1MA.03.5.10DT OPERACIONS EN FPOLAR

Operacions en forma polar

Suma i resta: es fa en forma binòmica

Multiplicació

Es multipliquen els mòduls i es sumen els arguments

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mrow»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»§#176;«/mo»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mrow»«mi mathvariant=¨bold¨»§#946;«/mi»«mo mathvariant=¨bold¨»§#176;«/mo»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»rs«/mi»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»§#946;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#176;«/mo»«/mrow»«/msub»«/math»
si l'angle és superior a 360º, cal restar k·360º.

Divisió

Es divideixen els mòduls i es resten els graus:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mrow»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»§#176;«/mo»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mrow»«mi mathvariant=¨bold¨»§#946;«/mi»«mo mathvariant=¨bold¨»§#176;«/mo»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«msub mathcolor=¨#003300¨»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»r«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»§#946;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#176;«/mo»«/mrow»«/msub»«/math»
si l'angle és negatiu, cal sumar-li 360º.

Potència

S'eleva el mòdul i es multiplica l'argument

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#003300¨»«mfenced mathcolor=¨#003300¨»«msub»«mi mathvariant=¨bold¨»r«/mi»«mrow»«mi mathvariant=¨bold¨»§#945;«/mi»«mo»§#176;«/mo»«/mrow»«/msub»«/mfenced»«mi mathvariant=¨bold¨»n«/mi»«/msup»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#0033F00¨»§#160;«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msup»«msub mathcolor=¨#003300¨»«mo mathcolor=¨#003300¨»§#160;«/mo»«mrow»«mi mathvariant=¨bold¨»n§#945;«/mi»«mo»§#176;«/mo»«/mrow»«/msub»«/math»

si l'angle és superior a 360º, cal restar k·360º.

]]> 0.0000000 0.0000000 0 1MA.03.5.11Q F.POLAR: multiplicació Calcula el mòdul i l'argument del producte:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«msub mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«msub mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»s«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«/mstyle»«/math»

Format de la resposta:
r=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»2«/mn»«/msqrt»«/math»
a=330

]]> 1.0000000 0.5000000 0 0 r=#ra=#a]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>a_2</mi><mo>+</mo><mi>b_2</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfenced close="&Verbar;" open="&Verbar;"><mi>x_1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mfenced close="&Verbar;" open="&Verbar;"><mi>x_2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>359</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>359</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>r_1</mi><mo>*</mo><mi>r_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>q</mi><mo>+</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a_5</mi><mo><</mo><mn>360</mn></mrow><mrow><mi>a</mi><mo>=</mo><mi>a_5</mi></mrow><mrow><mi>a</mi><mo>=</mo><mi>a_5</mi><mo>-</mo><mn>360</mn></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>-</mo><mn>5</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>-</mo><mn>4</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>61</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>250</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>253</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msqrt><mn>305</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>143</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mo>#</mo><mi>r</mi><mspace linebreak="newline"/><mi>a</mi><mo>=</mo><mo>#</mo><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question> Es multipliquen els mòduls i es simplifica, si s'escau.
Es sumen els angles: si el resultat és negatiu, sumem 360º; si el resultat és superior a 360º, cal restar 360º tants cops com sigui necessari per donar el resultat en la 1a volta.

]]> 1MA.03.5.15Q F.POLAR: Multiplicació (trobar r) Calcula r si
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»r«/mi»«msub mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«msub mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»s«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»r«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«/mstyle»«/math»

Format de la resposta:
r=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»2«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 r=#sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>a_2</mi><mo>+</mo><mi>b_2</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfenced close="&Verbar;" open="&Verbar;"><mi>x_1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mfenced close="&Verbar;" open="&Verbar;"><mi>x_2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>359</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>359</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>r_1</mi><mo>*</mo><mi>r_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>q</mi><mo>+</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a_5</mi><mo><</mo><mn>360</mn></mrow><mrow><mi>a</mi><mo>=</mo><mi>a_5</mi></mrow><mrow><mi>a</mi><mo>=</mo><mi>a_5</mi><mo>-</mo><mn>360</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>r_1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>7</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>-</mo><mn>2</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>+</mo><mn>7</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>17</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>211</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>293</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>*</mo><msqrt><mn>34</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>144</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>17</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="check_rationalized"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Es divideixen els mòduls i es simplifica, si s'escau.

]]> 1MA.03.5.21Q F.POLAR: divisió Calcula el mòdul i l'argument del quocient:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r_«/mi»«mn mathvariant=¨bold¨»1«/mn»«msub»«mo mathvariant=¨bold¨»§#160;«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«/mrow»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r_«/mi»«mn mathvariant=¨bold¨»2«/mn»«msub»«mo mathvariant=¨bold¨»§#160;«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»s«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«/mrow»«/mfrac»«/mstyle»«/math»

Format de la resposta:
r=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»2«/mn»«/msqrt»«/math»
a=330

]]> 1.0000000 0.5000000 0 0 r=#ra=#a]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>a_2</mi><mo>+</mo><mi>b_2</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfenced close="&Verbar;" open="&Verbar;"><mi>x_1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mfenced close="&Verbar;" open="&Verbar;"><mi>x_2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>359</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>359</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfrac><mi>r_1</mi><mi>r_2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>q</mi><mo>-</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a_5</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>a</mi><mo>=</mo><mi>a_5</mi><mo>+</mo><mn>360</mn></mrow><mrow><mi>a</mi><mo>=</mo><mi>a_5</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>+</mo><mn>2</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>-</mo><mn>8</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>104</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>149</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>5</mn></msqrt><mn>10</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>315</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mo>#</mo><mi>r</mi><mspace linebreak="newline"/><mi>a</mi><mo>=</mo><mo>#</mo><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question> Es divideixen els mòduls i es simplifica, si s'escau.
Es resten els angles: si el resultat és negatiu, sumem 360º; si el resultat és superior a 360º, cal restar 360º tants cops com sigui necessari per donar el resultat en la 1a volta.

]]> 1MA.03.5.25Q F.POLAR: divisió (trobar z) Troba el mòdul i l'argument de z (en la 1a volta) si:
_{«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨18px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»z«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r_«/mi»«msub»«mn mathvariant=¨bold¨»2«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»s«/mi»«/mrow»«/msub»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msub»«/mrow»«/mstyle»«/math»}

Format de la resposta:
r=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»2«/mn»«/msqrt»«/math»
a=330

]]> 1.0000000 0.5000000 0 0 r=#r1a=#q]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>a_2</mi><mo>+</mo><mi>b_2</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mfenced close="&Verbar;" open="&Verbar;"><mi>x_1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mfenced close="&Verbar;" open="&Verbar;"><mi>x_2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>359</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>359</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfrac><mi>r1</mi><mi>r_2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>q</mi><mo>-</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a_5</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>a</mi><mo>=</mo><mi>a_5</mi><mo>+</mo><mn>360</mn></mrow><mrow><mi>a</mi><mo>=</mo><mi>a_5</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>+</mo><mn>3</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>+</mo><mn>9</mn><mo>*</mo><imaginaryi/></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>317</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>217</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>2</mn></msqrt><mn>18</mn></mfrac><mo>*</mo><mi>r_1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><mi>a</mi><mo>=</mo><mo>#</mo><mi>q</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question> Es multipliquen els mòduls i es sumen els arguments. Si s'escau es passa a la 1a volta.

]]> 1MA.03.5.31 F.POLAR: potència Calcula el mòdul i l'argument de la potència:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r_«/mi»«msub mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math»

Format de la resposta:
r=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»2«/mn»«/msqrt»«/math»
a=330

]]> 1.0000000 0.5000000 0 0 r=#ra=#a]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>a_2</mi><mo>+</mo><mi>b_2</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfenced close="&Verbar;" open="&Verbar;"><mi>x_1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mfenced close="&Verbar;" open="&Verbar;"><mi>x_2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>359</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>359</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msup><mfenced><mi>r_1</mi></mfenced><mi>n</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>q</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a_5</mi><mo><</mo><mn>360</mn></mrow><mrow><mi>a</mi><mo>=</mo><mi>a_5</mi></mrow><mrow><mi>a</mi><mo>=</mo><mi>a_5</mi><mo> </mo><mi>mod</mi><mo> </mo><mn>360</mn></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6588344</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>207</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mo>#</mo><mi>r</mi><mspace linebreak="newline"/><mi>a</mi><mo>=</mo><mo>#</mo><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question> S'eleva el mòdul a #n i es simplifica, si s'escau.
Es multiplica l'angle per n: si el resultat és negatiu, sumem 360º; si el resultat és superior a 360º, cal restar 360º tants cops com sigui necessari per donar el resultat en la 1a volta.]]> 1MA.03.5.42Q F.POLAR: Potència(polar i binòmica) Calcula (#r_1 _{#q º} )^#n

a) quin és el seu mòdul

b) quin és el seu argument

c) quina és la seva forma binòmica
Format de la resposta:
r=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»2«/mn»«/msqrt»«/math»
a=330
z: coeficients als deumil·lèsims

]]> 1.0000000 0.5000000 0 0 r=#ra=#az=#z1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfenced close="&Verbar;" open="&Verbar;"><mi>x_1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>359</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msup><mfenced><mi>r_1</mi></mfenced><mi>n</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_5</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>q</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a_5</mi><mo><</mo><mn>360</mn></mrow><mrow><mi>a</mi><mo>=</mo><mi>a_5</mi></mrow><mrow><mi>a</mi><mo>=</mo><mi>a_5</mi><mo> </mo><mi>mod</mi><mo> </mo><mn>360</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><mi>r</mi><mo>*</mo><mo>(</mo><mi>cos</mi><mfenced><mrow><mi>a</mi><mo>*</mo><mfrac><pi/><mn>180</mn></mfrac></mrow></mfenced><mo>+</mo><mfenced><mrow><mi>sin</mi><mfenced><mrow><mi>a</mi><mo>*</mo><mfrac><pi/><mn>180</mn></mfrac></mrow></mfenced><mo>*</mo><imaginaryi/></mrow></mfenced><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>5</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>33</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>66</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.0337</mn><mo>+</mo><mn>4.5677</mn><mo>*</mo><imaginaryi/></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mo>#</mo><mi>r</mi><mspace linebreak="newline"/><mi>a</mi><mo>=</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>z</mi><mo>=</mo><mo>#</mo><mi>z</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="answer_parameter">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question> S'eleva el mòdul a #n i es simplifica, si s'escau.
Es multiplica l'angle per n: si el resultat és negatiu, sumem 360º; si el resultat és superior a 360º, cal restar 360º tants cops com sigui necessari per donar el resultat en la 1a volta.

]]> 1MA.03.5.50DT ARREL ENÈSIMA (FPOLAR)

Arrel enèsima en forma polar

Per a calcular l'arrel enèsima d'un nombre en forma polar:

el mòdul de l'arrel enèsima és l'arrel enèsima del mòdul: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»r«/mi»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«/math»
els arguments de les n diferents arrels es calculen amb: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»§#176;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»k«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»360«/mn»«mo mathvariant=¨bold¨»§#176;«/mo»«/mrow»«mi mathvariant=¨bold¨»n«/mi»«/mfrac»«/math»
es van donant valors a k, des de 0 fins a n-1 per trobar els n angles de la resposta.

]]> 0.0000000 0.0000000 0 1MA.03.5.51Q F.POLAR: arrel d'índex 3 Calcula el mòdul i els 3 arguments de l'arrel d'índex 3 del nombre:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«msub mathcolor=¨#003300¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

Format de la resposta (SENSE unitats):
r=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»2«/mn»«/msqrt»«/math»
arguments={20,140,260} amb CLAUS

]]> 1.0000000 0.5000000 0 0 r=#rarguments=#arg]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>a_11</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfenced close="&Verbar;" open="&Verbar;"><mi>x_1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>89</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mroot><mi>r_1</mi><mi>n</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mrow><mi>k</mi><mo>·</mo><mn>360</mn><mo>+</mo><mn>30</mn></mrow><mn>7</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfrac><mrow><mi>q</mi><mo>+</mo><mi>k</mi><mo>·</mo><mn>360</mn></mrow><mn>4</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mi>q</mi><mn>3</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mi>q</mi><mn>3</mn></mfrac><mo>+</mo><mn>120</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfrac><mi>q</mi><mn>3</mn></mfrac><mo>+</mo><mn>240</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>arg</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msqrt><mn>10</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>87</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>90</mn><mn>6</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>360</mn><mn>7</mn></mfrac><mo>*</mo><mi>k</mi><mo>+</mo><mfrac><mn>30</mn><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>arg</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>29</mn><mo>,</mo><mn>149</mn><mo>,</mo><mn>269</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mo>#</mo><mi>r</mi><mspace linebreak="newline"/><mi>a</mi><mi>r</mi><mi>g</mi><mi>u</mi><mi>m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>a</mi><mi>r</mi><mi>g</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="answer_parameter">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question> Pel mòdul es calcula l'arrel d'índex 3.
Per l'argument, cal dividir #qº + k·360º per 3, i anar substituint k per 0,1,2.

]]> 1MA.03.5.52Q F.POLAR: Arrel índex 4 Calcula el mòdul i els 4 arguments de l'arrel d'índex 4 del nombre:

(#r_1 _{#q º} )

Format de la resposta (SENSE unitats):
r=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«msqrt»«mn»2«/mn»«/msqrt»«/math»
arguments={20, 110, 200, 290}

]]> 1.0000000 0.5000000 0 0 r=#rarguments=#arg]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>a_11</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfenced close="&Verbar;" open="&Verbar;"><mi>x_1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mn>4</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>89</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mroot><mi>r_1</mi><mi>n</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mrow><mi>k</mi><mo>·</mo><mn>360</mn><mo>+</mo><mn>30</mn></mrow><mn>7</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfrac><mrow><mi>q</mi><mo>+</mo><mi>k</mi><mo>·</mo><mn>360</mn></mrow><mn>4</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mi>q</mi><mn>4</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mi>q</mi><mn>4</mn></mfrac><mo>+</mo><mn>90</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfrac><mi>q</mi><mn>4</mn></mfrac><mo>+</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mfrac><mi>q</mi><mn>4</mn></mfrac><mo>+</mo><mn>270</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>arg</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>29</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>140</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>29</mn><mn>8</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>360</mn><mn>7</mn></mfrac><mo>*</mo><mi>k</mi><mo>+</mo><mfrac><mn>30</mn><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>125</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>215</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>305</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>arg</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>35</mn><mo>,</mo><mn>125</mn><mo>,</mo><mn>215</mn><mo>,</mo><mn>305</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mo>#</mo><mi>r</mi><mspace linebreak="newline"/><mi>a</mi><mi>r</mi><mi>g</mi><mi>u</mi><mi>m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>a</mi><mi>r</mi><mi>g</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question> Pel mòdul es calcula l'arrel d'índex 4.
Per l'argument, cal dividir #qº + k·360º per 4, i anar substituint k per 0,1,2,3.]]> 1MA.03.5.55Q F.POLAR: arrel índex aleatori Calcula el mòdul i l'argument del nombre: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#003300¨»«msub»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mroot»«/mstyle»«/math»

Format de la resposta:
r=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn»3«/mn»«msqrt»«mn»2«/mn»«/msqrt»«/mrow»«/mstyle»«/math»
a=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 r=#ra=#a]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfenced close="‖" open="‖"><mi>x_1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>359</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mroot><mi>r_1</mi><mi>n</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mrow><mi>k</mi><mo>·</mo><mn>360</mn><mo>+</mo><mn>30</mn></mrow><mn>7</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfrac><mrow><mi>q</mi><mo>+</mo><mi>k</mi><mo>·</mo><mn>360</mn></mrow><mi>n</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>294</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>45</mn><mn>8</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>360</mn><mn>7</mn></mfrac><mo>*</mo><mi>k</mi><mo>+</mo><mfrac><mn>30</mn><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>90</mn><mo>*</mo><mi>k</mi><mo>+</mo><mfrac><mn>147</mn><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mo>#</mo><mi>r</mi><mspace linebreak="newline"/><mi>a</mi><mo>=</mo><mo>#</mo><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question> r: Es calcula l'arrel d'índex #n del mòdul del nombre.
a: Cal dividir #q º + k·360º per #n]]> 1MA.03.5.61Q F.POLARTrobar 3 altres arrels sabent arrel n-èsima «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»t«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«/mrow»«/mstyle»«/math» és una de les arrels d'índex 4 d'un nombre z. Escriu el mòdul i els arguments de les altres 3 arrels.

Format de les respostes:
||z||=«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mn»2«/mn»«/msqrt»«/math»

arguments={15,70,105}

]]> 1.0000000 0.5000000 0 0 z=#sol1arguments=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>b_1</mi><mo>*</mo><imaginaryi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mfenced close="‖" open="‖"><mi>x_1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mroot><mi>r_1</mi><mn>4</mn></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mn>4</mn><mo>*</mo><mi>aleatori</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>89</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t21</mi><mo>=</mo><mi>t1</mi><mo>+</mo><mn>90</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t31</mi><mo>=</mo><mi>t1</mi><mo>+</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t41</mi><mo>=</mo><mi>t1</mi><mo>+</mo><mn>270</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t1</mi><mo>></mo><mn>270</mn></mrow><mtable><mtr><mtd><mi>t2</mi><mo>=</mo><mi>t21</mi><mo>-</mo><mn>360</mn></mtd></mtr><mtr><mtd><mi>t3</mi><mo>=</mo><mi>t31</mi><mo>-</mo><mn>360</mn></mtd></mtr><mtr><mtd><mi>t4</mi><mo>=</mo><mi>t41</mi><mo>-</mo><mn>360</mn></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t1</mi><mo>></mo><mn>180</mn></mrow><mtable><mtr><mtd><mi>t2</mi><mo>=</mo><mi>t21</mi></mtd></mtr><mtr><mtd><mi>t3</mi><mo>=</mo><mi>t31</mi><mo>-</mo><mn>360</mn></mtd></mtr><mtr><mtd><mi>t4</mi><mo>=</mo><mi>t41</mi><mo>-</mo><mn>360</mn></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t1</mi><mo>></mo><mn>90</mn></mrow><mtable><mtr><mtd><mi>t2</mi><mo>=</mo><mi>t21</mi></mtd></mtr><mtr><mtd><mi>t3</mi><mo>=</mo><mi>t31</mi></mtd></mtr><mtr><mtd><mi>t4</mi><mo>=</mo><mi>t41</mi><mo>-</mo><mn>360</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>t2</mi><mo>=</mo><mi>t21</mi></mtd></mtr><mtr><mtd><mi>t3</mi><mo>=</mo><mi>t31</mi></mtd></mtr><mtr><mtd><mi>t4</mi><mo>=</mo><mi>t41</mi></mtd></mtr></mtable></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>t2</mi><mo>,</mo><mi>t3</mi><mo>,</mo><mi>t4</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>74</mn><mn>8</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>140</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>230</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>320</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|" close="|"><mfenced open="|" close="|"><mi>z</mi></mfenced></mfenced><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>a</mi><mi>r</mi><mi>g</mi><mi>u</mi><mi>m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="inputCompound">true</data><data name="casSession"/></localData></question> Mòdul: El mòdul és el mateix per totes les arrels.
Arguments: per trobar els altres arguments, n'hi ha prou amb sumar 360º/4 reiteradament.]]> 1MA.03.5.71Q Trobar afixos pentàgon Escriu en forma polar els afixos dels altres 4 vèrtex del pentàgon, si el vèrtex del 1r quadrant és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«msub mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/msub»«/math»

Format:

||z|| = mòdul de tots els afixos.

arguments ={20,30,40,50}

]]> 1.0000000 0.5000000 0 0 ||z||=#solarguments =#sol6]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>17</mn><mo>,</mo><mn>19</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><msqrt><mi>r</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>9</mn><mo>,</mo><mn>39</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>r1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mn>72</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>sol2</mi><mo>+</mo><mn>72</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>sol3</mi><mo>+</mo><mn>72</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol5</mi><mo>=</mo><mi>sol4</mi><mo>+</mo><mn>72</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol6</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>sol2</mi><mo>,</mo><mi>sol3</mi><mo>,</mo><mi>sol4</mi><mo>,</mo><mi>sol5</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>108</mn><mo>,</mo><mn>180</mn><mo>,</mo><mn>252</mn><mo>,</mo><mn>324</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>|</mo><mo>|</mo><mi>z</mi><mo>|</mo><mo>|</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mi>a</mi><mi>r</mi><mi>g</mi><mi>u</mi><mi>m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi>s</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>6</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El mòdul és el mateix, ja que el radi de la circumferència no canvia.

L'argument, en un pentàgon, va augmentant de 360º/5.

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