Números complejos 7.1 - Complejos - F - Ecuación en C Encuentre todas las soluciones para z en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#8450;«/mi»«/math» tales que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»A«/mi»«mover»«mi»z«/mi»«mo»§#175;«/mo»«/mover»«mo»+«/mo»«mo»#«/mo»«mi»B«/mi»«mfenced open=¨|¨ close=¨|¨»«mi»z«/mi»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»D«/mi»«mo»+«/mo»«mo»#«/mo»«mi»E«/mi»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»i«/mi»«/math»

Entregue el mayor valor posible para la parte real de z.

]]> 1.0000000 0.3333333 0 0 #sol Exprese z en su forma algebraica, desarrolle e iguale las partes reales en la ecuación.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨|¨ close=¨|¨»«mfrac»«mrow»«mo»(«/mo»«mi»A«/mi»«mo»+«/mo»«mo»#«/mo»«mi»u«/mi»«mo»§#160;«/mo»«mi»i«/mi»«msup»«mo»)«/mo»«mn»3«/mn»«/msup»«/mrow»«mrow»«mo»(«/mo»«mo»#«/mo»«mi»v«/mi»«mo»+«/mo»«mo»#«/mo»«mi»w«/mi»«mo»§#160;«/mo»«mi»i«/mi»«msup»«mo»)«/mo»«mn»2«/mn»«/msup»«/mrow»«/mfrac»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»N«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 (a) RE(z)=#sol1(b) IM(z)=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="es" 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>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang</mi><mo>=</mo><mi>aleatorio</mi><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><mn>7</mn><mo>,</mo><mn>8</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>14</mn><mo>,</mo><mn>15</mn><mo>}</mo><mo>*</mo><mfrac><pi/><mn>12</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>r</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>r</mi><mo>*</mo><mi>sen</mi><mo>(</mo><mi>ang</mi><mo>)</mo></math></input></command></group></library><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>a</mi><mo>)</mo><mo> </mo><mi>R</mi><mi>E</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mo>(</mo><mi>b</mi><mo>)</mo><mo> </mo><mi>I</mi><mi>M</mi><mo>(</mo><mi>z</mi><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^(-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> 7.5 Complejos-M-Raíces enésimas de la unidad Calcular «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»1«/mn»«mo»+«/mo»«mn»2«/mn»«mi»§#949;«/mi»«mo»+«/mo»«mn»3«/mn»«msup»«mi»§#949;«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mo»§#8943;«/mo»«mo»+«/mo»«mo»#«/mo»«mi»n«/mi»«mo»§#160;«/mo»«msup»«mi»§#949;«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/msup»«/math», donde «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#949;«/mi»«/math» es la #n-ésima raíz de 1 («math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#949;«/mi»«/math» distinto de 1).

Importante: No olvide escribir los paréntesis de llaves.

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="es" 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>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/><mo>)</mo><mo>*</mo><mi>z</mi><mo>+</mo><mo>(</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>*</mo><imaginaryi/><mo>)</mo><mo>=</mo><mo>(</mo><mi>e</mi><mo>+</mo><mi>f</mi><mo>*</mo><imaginaryi/><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>resolver</mi><mo>(</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/><mo>)</mo><mo>*</mo><mi>z</mi><mo>+</mo><mo>(</mo><mi>c</mi><mo>+</mo><mi>d</mi><mo>*</mo><imaginaryi/><mo>)</mo><mo>-</mo><mo>(</mo><mi>e</mi><mo>+</mo><mi>f</mi><mo>*</mo><imaginaryi/><mo>)</mo><mo>,</mo><complexes/><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>=</mo><mi>sol</mi><mo>)</mo><mo>?</mo></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"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>z</mi><mo>=</mo><mo>-</mo><mfrac><mn>7</mn><mn>13</mn></mfrac><mo>+</mo><mfrac><mrow><mn>17</mn><mo>*</mo><imaginaryi/></mrow><mn>13</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group><group><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>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>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">test</param></assertion></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Complejos. Raíz n-ésima de un número complejo Al calcular las raíces n-ésimas de un número complejo «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»z«/mi»«/math» y luego ubicarlas en un plano complejo se obtiene un polígono regular de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«/math» lados centrado en el origen. Escriba las coordenadas exactas del vértice marcado en rojo en el siguiente gráfico:

#graf

Sabiendo que los vértices del polígono se encuentran en el conjunto solución de la ecuación:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»z«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«mn»1«/mn»«/mrow»«/msup»«mo»=«/mo»«mo»#«/mo»«mi»z«/mi»«mn»1«/mn»«/math»

Observación: el número complejo que se pide como respuesta se puede escribir de las siguientes formas:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»§#183;«/mo»«msup»«mi»e«/mi»«mrow»«mi»§#952;«/mi»«mo»§#183;«/mo»«mi»i«/mi»«/mrow»«/msup»«/math» forma de euler.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»§#183;«/mo»«mfenced»«mrow»«mi»cos«/mi»«mo»(«/mo»«mi»§#952;«/mi»«mo»)«/mo»«mo»+«/mo»«mi»i«/mi»«mo»§#183;«/mo»«mi»s«/mi»«mi»e«/mi»«mi»n«/mi»«mo»(«/mo»«mi»§#952;«/mi»«mo»)«/mo»«/mrow»«/mfenced»«/math» forma polar.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»+«/mo»«mi»i«/mi»«mo»§#183;«/mo»«mi»b«/mi»«/math» forma cartesiana.

]]> 1.0000000 0.3333333 0 0 #r1#n1·e#u1·i]]> #sol Esta es una aproximación, no es el valor exacto.

]]> <question><wirisCasSession><![CDATA[<session lang="es" 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>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>aleatorio</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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n1</mi><mo>∈</mo><mo>{</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>}</mo></mrow><mrow><mi>a1</mi><mo>=</mo><pi/><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>0</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><mn>1</mn><mo>}</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n1</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>a1</mi><mo>=</mo><pi/><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><mn>1</mn><mo>}</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n1</mi><mo>=</mo><mn>6</mn></mrow><mrow><mi>a1</mi><mo>=</mo><pi/><mo>*</mo><mi>aleatorio</mi><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></mrow><mrow><mi>a1</mi><mo>=</mo><mn>0</mn></mrow></apply></apply></apply></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"><mi>d1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>distancia</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mroot><mi>r1</mi><mi>n1</mi></mroot><mo>*</mo><mi>cos</mi><mfenced><mfrac><mrow><mn>1</mn><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></mfenced><mo>,</mo><mroot><mi>r1</mi><mi>n1</mi></mroot><mo>*</mo><mi>sen</mi><mfenced><mfrac><mrow><mn>1</mn><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></mfenced></mrow></mfenced><mo>,</mo><mi>punto</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>t1</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mi>punto</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mn>2</mn><mo>.</mo><mn>2</mn><mo>*</mo><mi>d1</mi><mo>,</mo><mn>2</mn><mo>.</mo><mn>2</mn><mo>*</mo><mi>d1</mi><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">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>en</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n1</mi></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>P</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>P</mi><mo>=</mo><mi>punto</mi><mfenced><mrow><mroot><mi>r1</mi><mi>n1</mi></mroot><mo>*</mo><mi>cos</mi><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></mfenced><mo>,</mo><mroot><mi>r1</mi><mi>n1</mi></mroot><mo>*</mo><mi>sen</mi><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>graf</mi><mo>=</mo><mi>dibujar</mi><mo>(</mo><mi>P</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo> </mo><mi>en</mi><mo> </mo><mn>1</mn><mo>.</mo><mo>.</mo><mo>(</mo><mi>n1</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>Q</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>Q</mi><mo>=</mo><mi>segmento</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mroot><mi>r1</mi><mi>n1</mi></mroot><mo>*</mo><mi>cos</mi><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></mfenced><mo>,</mo><mroot><mi>r1</mi><mi>n1</mi></mroot><mo>*</mo><mi>sen</mi><mfenced><mfrac><mrow><mi>i</mi><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></mfenced></mrow></mfenced><mo>,</mo><mi>punto</mi><mfenced><mrow><mroot><mi>r1</mi><mi>n1</mi></mroot><mo>*</mo><mi>cos</mi><mfenced><mfrac><mrow><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></mfenced><mo>,</mo><mroot><mi>r1</mi><mi>n1</mi></mroot><mo>*</mo><mi>sen</mi><mfenced><mfrac><mrow><mo>(</mo><mi>i</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></mfenced></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>dibujar</mi><mo>(</mo><mi>Q</mi><mo>)</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mfenced><mrow><mi>segmento</mi><mfenced><mrow><mi>punto</mi><mfenced><mrow><mroot><mi>r1</mi><mi>n1</mi></mroot><mo>*</mo><mi>cos</mi><mfenced><mfrac><mrow><mn>1</mn><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></mfenced><mo>,</mo><mroot><mi>r1</mi><mi>n1</mi></mroot><mo>*</mo><mi>sen</mi><mfenced><mfrac><mrow><mn>1</mn><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></mfenced></mrow></mfenced><mo>,</mo><mi>punto</mi><mfenced><mrow><mroot><mi>r1</mi><mi>n1</mi></mroot><mo>*</mo><mi>cos</mi><mfenced><mfrac><mrow><mi>n1</mi><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></mfenced><mo>,</mo><mroot><mi>r1</mi><mi>n1</mi></mroot><mo>*</mo><mi>sen</mi><mfenced><mfrac><mrow><mi>n1</mi><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></mfenced></mrow></mfenced></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X1</mi><mo>=</mo><mi>cos</mi><mfenced><mfrac><mrow><mi>w1</mi><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y1</mi><mo>=</mo><mi>sen</mi><mfenced><mfrac><mrow><mi>w1</mi><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></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>n1</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mi>n1</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mi>n1</mi><mo>)</mo></mrow><mrow><mi>X1</mi><mo>*</mo><mi>Y1</mi><mo>≠</mo><mn>0</mn></mrow></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></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><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mfrac><mrow><mi>w1</mi><mo>*</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>a1</mi></mrow><mi>n1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mroot><mi>r1</mi><mi>n1</mi></mroot><mo>*</mo><msup><exponentiale/><mrow><mi>u1</mi><mo>*</mo><imaginaryi/></mrow></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>graf</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</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>t2</mi><mo>=</mo><mi>tablero</mi><mo>(</mo><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dibujar</mi><mo>(</mo><mi>t2</mi><mo>,</mo><mn>1</mn><mo>+</mo><imaginaryi/><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tablero2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.0905</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</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi></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><mfrac><mroot><mn>32</mn><mn>8</mn></mroot><mn>2</mn></mfrac><mo>+</mo><mfrac><mrow><mroot><mn>32</mn><mn>8</mn></mroot><mo>*</mo><imaginaryi/></mrow><mn>2</mn></mfrac></math></output></command></group><group><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"><mroot><mrow><mo>#</mo><mi>r</mi><mn>1</mn></mrow><mrow><mo>#</mo><mi>n</mi><mn>1</mn></mrow></mroot><mo>·</mo><msup><mi mathvariant="normal">e</mi><mrow><mo>#</mo><mi>u</mi><mn>1</mn><mo>·</mo><mi mathvariant="normal">i</mi></mrow></msup></math>]]></correctAnswer><correctAnswer id="1">#sol</correctAnswer></correctAnswers><assertions><assertion name="check_no_more_decimals"><param name="digits">0</param></assertion><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-1)</option><option name="relative_tolerance">true</option><option name="precision">5</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> Complejos. Solución no única de una ecuación Encuentre un número complejo «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»z«/mi»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8450;«/mi»«/math» tal que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»R«/mi»«mi»e«/mi»«mo»(«/mo»«mi»z«/mi»«mo»)«/mo»«mo»§#8800;«/mo»«mn»0«/mn»«mo»§#160;«/mo»«mo»§#8743;«/mo»«mo»§#160;«/mo»«mi»I«/mi»«mi»m«/mi»«mo»(«/mo»«mi»z«/mi»«mo»)«/mo»«mo»§#8800;«/mo»«mn»0«/mn»«/math» y que satisfaga la siguiente igualdad:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mfenced open=¨|¨ close=¨|¨»«mi»z«/mi»«/mfenced»«mrow»«mo»#«/mo»«mi»m«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»m«/mi»«mn»1«/mn»«/mrow»«mfenced open=¨|¨ close=¨|¨»«mi»z«/mi»«/mfenced»«/mfrac»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»e«/mi»«mi»c«/mi»«mn»1«/mn»«mo»=«/mo»«mo»#«/mo»«mi»e«/mi»«mi»c«/mi»«mn»2«/mn»«/math»

]]> 1.0000000 0.3333333 0 0 z=#sol]]> <question><wirisCasSession><![CDATA[<session lang="es" 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>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr></mtable><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a2</mi><mn>2</mn></msup><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec1</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>z</mi><mo>+</mo><mi>a1</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec2</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>z</mi><mo>+</mo><mi>a2</mi><mo>*</mo><imaginaryi/></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>a1</mi><mo>*</mo><mi>a2</mi><mo>></mo><mn>0</mn><mo>∧</mo><mfrac><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a2</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mo>*</mo><mi>a2</mi></mrow></mfrac><mo>></mo><mn>0</mn></mrow><mrow><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>*</mo><mi>a2</mi><mo>></mo><mn>0</mn><mo>∧</mo><mfrac><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a2</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mo>*</mo><mi>a2</mi></mrow></mfrac><mo><</mo><mn>0</mn></mrow><mrow><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>*</mo><mi>a2</mi><mo><</mo><mn>0</mn><mo>∧</mo><mfrac><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a2</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mo>*</mo><mi>a2</mi></mrow></mfrac><mo><</mo><mn>0</mn></mrow><mrow><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>}</mo></mrow><mrow><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo></mrow></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mo>"</mo><mi>Re</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>></mo><mn>0</mn><mo>"</mo><mo>,</mo><mn>2</mn><mo>→</mo><mo>"</mo><mi>Re</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>"</mo><mo>,</mo><mn>3</mn><mo>→</mo><mo>"</mo><mi>Re</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>"</mo><mo>,</mo><mn>4</mn><mo>→</mo><mo>"</mo><mi>Re</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>></mo><mn>0</mn><mo>"</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R2</mi><mo>=</mo><mo>{</mo><mn>1</mn><mo>→</mo><mo>"</mo><mi>Im</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>></mo><mn>0</mn><mo>"</mo><mo>,</mo><mn>2</mn><mo>→</mo><mo>"</mo><mi>Im</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>></mo><mn>0</mn><mo>"</mo><mo>,</mo><mn>3</mn><mo>→</mo><mo>"</mo><mi>Im</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>"</mo><mo>,</mo><mn>4</mn><mo>→</mo><mo>"</mo><mi>Im</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>"</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C1</mi><mo>=</mo><mi>R1</mi><mo>(</mo><mi>w1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C2</mi><mo>=</mo><mi>R2</mi><mo>(</mo><mi>w1</mi><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">if</csymbol><mrow><mi>w1</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>funcal</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>:</mo><mo>=</mo><mfenced><mrow><mfenced close="|" open="|"><mrow><mi>z</mi><mo>+</mo><mi>a1</mi></mrow></mfenced><mo>=</mo><mfenced close="|" open="|"><mrow><mi>z</mi><mo>+</mo><mi>a2</mi><mo>*</mo><imaginaryi/></mrow></mfenced><mo>∧</mo><mi>parte_real</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>></mo><mn>0</mn><mo>∧</mo><mi>parte_imaginaria</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>></mo><mn>0</mn></mrow></mfenced><mo>?</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>w1</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>funcal</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>:</mo><mo>=</mo><mfenced><mrow><mfenced close="|" open="|"><mrow><mi>z</mi><mo>+</mo><mi>a1</mi></mrow></mfenced><mo>=</mo><mfenced close="|" open="|"><mrow><mi>z</mi><mo>+</mo><mi>a2</mi><mo>*</mo><imaginaryi/></mrow></mfenced><mo>∧</mo><mi>parte_real</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>∧</mo><mi>parte_imaginaria</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>></mo><mn>0</mn></mrow></mfenced><mo>?</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>w1</mi><mo>=</mo><mn>3</mn></mrow><mrow><mi>funcal</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>:</mo><mo>=</mo><mfenced><mrow><mfenced close="|" open="|"><mrow><mi>z</mi><mo>+</mo><mi>a1</mi></mrow></mfenced><mo>=</mo><mfenced close="|" open="|"><mrow><mi>z</mi><mo>+</mo><mi>a2</mi><mo>*</mo><imaginaryi/></mrow></mfenced><mo>∧</mo><mi>parte_real</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>∧</mo><mi>parte_imaginaria</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo><</mo><mn>0</mn></mrow></mfenced><mo>?</mo></mrow><mrow><mi>funcal</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>:</mo><mo>=</mo><mfenced><mrow><mfenced close="|" open="|"><mrow><mi>z</mi><mo>+</mo><mi>a1</mi></mrow></mfenced><mo>=</mo><mfenced close="|" open="|"><mrow><mi>z</mi><mo>+</mo><mi>a2</mi><mo>*</mo><imaginaryi/></mrow></mfenced><mo>∧</mo><mi>parte_real</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>></mo><mn>0</mn><mo>∧</mo><mi>parte_imaginaria</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo><</mo><mn>0</mn></mrow></mfenced><mo>?</mo></mrow></apply></apply></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="|" open="|"><mrow><mi>z</mi><mo>-</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="|" open="|"><mrow><mi>z</mi><mo>+</mo><mn>10</mn><mo>*</mo><imaginaryi/></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R1</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>Re(z)>0</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>z</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">funcal</param></assertion></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>