1MA 03. NOMBRES COMPLEXOS/1MA.03.3 F.binòmPolarTrigon 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

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