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La ecuación:
Ecuación (3x−36)⋅(x+8)=0
Ecuación x+y-4=0
Ecuación 4-x/7=x/9
Ecuación z^4=1
Expresar {x} en función de y en la ecuación:
4*x-1*y=-3
9*x+17*y=13
-2*x-19*y=3
6*x+17*y=-11
Expresiones idénticas
log(a^ dos *b^ tres)= cero
logaritmo de (a al cuadrado multiplicar por b al cubo ) es igual a 0
logaritmo de (a en el grado dos multiplicar por b en el grado tres) es igual a cero
log(a2*b3)=0
loga2*b3=0
log(a²*b³)=0
log(a en el grado 2*b en el grado 3)=0
log(a^2b^3)=0
log(a2b3)=0
loga2b3=0
loga^2b^3=0
log(a^2*b^3)=O
Expresiones con funciones
Logaritmo log
log(1/2)*x=2*x+5
log(x)/log(4)=16
log(x^2+y^2)=2^y
log(1)-x*(3)-log(1)-x*(2)=1/2
logo+1(x+3)=2

log(a^2*b^3)=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

   / 2  3\    
log\a *b / = 0

\log{\left(a^{2} b^{3} \right)} = 0

Simplificar

Gráfica

Respuesta rápida [src]

       /                                                                               /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\\                                                                                /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\
       |                                                                               |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      |||                                                                                |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      ||
       |          _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------|||           _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||
       |         /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2|||          /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2||
       |        /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ |||         /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||
       |       /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /||        /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|
       |      /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------||       /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|
       |     /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /|      /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /
       |  6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          |   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          
       |  \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                          |   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                          
b1 = I*|- ------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------
       \                                                                          2                                                                                                                                                      2                                                                           /                                                                           2                                                                                                                                                      2

b_{1} = i \left(- \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right) - \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}

       /                                                                               /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\\                                                                                /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\
       |                                                                               |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      |||                                                                                |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      ||
       |          _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------|||           _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||
       |         /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2|||          /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2||
       |        /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ |||         /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||
       |       /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /||        /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|
       |      /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------||       /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|
       |     /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /|      /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /
       |  6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          |   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          
       |  \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                          |   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                          
b2 = I*|- ------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------
       \                                                                          2                                                                                                                                                      2                                                                           /                                                                           2                                                                                                                                                      2

b_{2} = i \left(- \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right) + \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}

                                                                                  /     /                            2                    2         \\                                                                                  /     /                            2                    2         \\
                                                                                  |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                  |     |  -2*im(a)*re(a)          re (a)               im (a)      ||
             _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||             _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||
            /                                          2                          |     |                 2                   2                    2||            /                                          2                          |     |                 2                   2                    2||
           /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||           /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||
          /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|          /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|
b3 =     /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------| + I*    /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|
        /     |                 2                    2|                     4     \                                3                                 /        /     |                 2                    2|                     4     \                                3                                 /
     6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                               6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          
     \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                               \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/

b_{3} = i \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)} + \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}

b3 = i*((re(a)^2/(re(a)^2 + im(a)^2)^2 - im(a)^2/(re(a)^2 + im(a)^2)^2)^2 + 4*re(a)^2*im(a)^2/(re(a)^2 + im(a)^2)^4)^(1/6)*sin(atan2(-2*re(a)*im(a)/(re(a)^2 + im(a)^2^2, re(a)^2/(re(a)^2 + im(a)^2)^2 - im(a)^2/(re(a)^2 + im(a)^2)^2)/3) + ((re(a)^2/(re(a)^2 + im(a)^2)^2 - im(a)^2/(re(a)^2 + im(a)^2)^2)^2 + 4*re(a)^2*im(a)^2/(re(a)^2 + im(a)^2)^4)^(1/6)*cos(atan2(-2*re(a)*im(a)/(re(a)^2 + im(a)^2)^2, re(a)^2/(re(a)^2 + im(a)^2)^2 - im(a)^2/(re(a)^2 + im(a)^2)^2)/3))

Suma y producto de raíces [src]

suma

  /                                                                               /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\\                                                                                /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\     /                                                                               /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\\                                                                                /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\                                                                                                                                                                                                                                                                                                          
  |                                                                               |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      |||                                                                                |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      ||     |                                                                               |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      |||                                                                                |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                                                                                                                                                                                                                                          
  |          _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------|||           _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||     |          _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------|||           _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                                                                                                                                                                                                                                                                                                          
  |         /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2|||          /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2||     |         /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2|||          /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2||                                                                                                                                                                                                                                                                                                          
  |        /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ |||         /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||     |        /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ |||         /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||                                                                                /     /                            2                    2         \\                                                                                  /     /                            2                    2         \\
  |       /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /||        /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     |       /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /||        /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|                                                                                |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                  |     |  -2*im(a)*re(a)          re (a)               im (a)      ||
  |      /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------||       /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|     |      /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------||       /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|           _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||             _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||
  |     /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /|      /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /     |     /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /|      /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /          /                                          2                          |     |                 2                   2                    2||            /                                          2                          |     |                 2                   2                    2||
  |  6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          |   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                               |  6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          |   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||           /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||
  |  \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                          |   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                               |  \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                          |   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                  /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|          /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|
I*|- ------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------- + I*|- ------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------- +     /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------| + I*    /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|
  \                                                                          2                                                                                                                                                      2                                                                           /                                                                           2                                                                                                                                                      2                                                                                \                                                                          2                                                                                                                                                      2                                                                           /                                                                           2                                                                                                                                                      2                                                                                 /     |                 2                    2|                     4     \                                3                                 /        /     |                 2                    2|                     4     \                                3                                 /
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                               6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                               \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/

\left(i \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)} + \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}\right) + \left(\left(i \left(- \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right) + \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right) + \left(i \left(- \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right) - \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right)\right)

  /                                                                               /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\\     /                                                                               /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\\                                                                                                                                                      
  |                                                                               |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      |||     |                                                                               |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      |||                                                                                                                                                      
  |          _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------|||     |          _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------|||                                                                                                                                                      
  |         /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2|||     |         /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2|||                                                                                                                                                      
  |        /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ |||     |        /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ |||                                                                                  /     /                            2                    2         \\
  |       /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /||     |       /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /||                                                                                  |     |  -2*im(a)*re(a)          re (a)               im (a)      ||
  |      /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------||     |      /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------||             _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||
  |     /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /|     |     /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /|            /                                          2                          |     |                 2                   2                    2||
  |  6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          |     |  6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          |           /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||
  |  \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                          |     |  \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                          |          /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|
I*|- ------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|- ------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------| + I*    /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|
  \                                                                          2                                                                                                                                                      2                                                                           /     \                                                                          2                                                                                                                                                      2                                                                           /        /     |                 2                    2|                     4     \                                3                                 /
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/

i \left(- \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right) + i \left(- \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right) + i \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}

producto

/  /                                                                               /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\\                                                                                /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\\ /  /                                                                               /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\\                                                                                /     /                            2                    2         \\                                                                                      /     /                            2                    2         \\\                                                                                                                                                                                                                                                                                                          
|  |                                                                               |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      |||                                                                                |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      ||| |  |                                                                               |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      |||                                                                                |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                      |     |  -2*im(a)*re(a)          re (a)               im (a)      |||                                                                                                                                                                                                                                                                                                          
|  |          _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------|||           _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||| |  |          _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------|||           _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||                 _________________________________________________________________    |atan2|------------------, ------------------ - ------------------|||                                                                                                                                                                                                                                                                                                          
|  |         /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2|||          /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2||| |  |         /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2|||          /                                          2                          |     |                 2                   2                    2||                /                                          2                          |     |                 2                   2                    2|||                                                                                                                                                                                                                                                                                                          
|  |        /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ |||         /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||| |  |        /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ |||         /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||               /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||| /                                                                             /     /                            2                    2         \\                                                                                  /     /                            2                    2         \\\
|  |       /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /||        /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|| |  |       /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /||        /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|     ___      /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|| |                                                                             |     |  -2*im(a)*re(a)          re (a)               im (a)      ||                                                                                  |     |  -2*im(a)*re(a)          re (a)               im (a)      |||
|  |      /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------||       /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|| |  |      /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------||       /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------|   \/ 3 *    /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------|| |        _________________________________________________________________    |atan2|------------------, ------------------ - ------------------||             _________________________________________________________________    |atan2|------------------, ------------------ - ------------------|||
|  |     /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /|      /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /| |  |     /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /|      /     |                 2                    2|                     4     \                                3                                 /            /     |                 2                    2|                     4     \                                3                                 /| |       /                                          2                          |     |                 2                   2                    2||            /                                          2                          |     |                 2                   2                    2|||
|  |  6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          |   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          | |  |  6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          |   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                                   6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          | |      /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ ||           /  /        2                    2         \         2      2          |     |/  2        2   \   /  2        2   \    /  2        2   \ |||
|  |  \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                          |   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                          | |  |  \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                          |   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                                   \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                          | |     /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /|          /   |      re (a)               im (a)      |     4*im (a)*re (a)       |     \\im (a) + re (a)/   \im (a) + re (a)/    \im (a) + re (a)/ /||
|I*|- ------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------|*|I*|- ------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------|*|    /    |------------------ - ------------------|  + ------------------ *cos|------------------------------------------------------------------| + I*    /    |------------------ - ------------------|  + ------------------ *sin|------------------------------------------------------------------||
\  \                                                                          2                                                                                                                                                      2                                                                           /                                                                           2                                                                                                                                                      2                                                                           / \  \                                                                          2                                                                                                                                                      2                                                                           /                                                                           2                                                                                                                                                      2                                                                           / |   /     |                 2                    2|                     4     \                                3                                 /        /     |                 2                    2|                     4     \                                3                                 /|
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                               6 /      |/  2        2   \    /  2        2   \ |    /  2        2   \                                                                          |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    \\/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                               \/       \\im (a) + re (a)/    \im (a) + re (a)/ /    \im (a) + re (a)/                                                                          /

\left(i \left(- \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} - \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right) + \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right) \left(i \left(- \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} + \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right) - \frac{\sqrt{3} \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2} - \frac{\sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}}{2}\right) \left(i \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)} + \sqrt[6]{\left(\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}}\right)^{2} + \frac{4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{4}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}},\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} - \frac{\left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2}} \right)}}{3} \right)}\right)

             2        2                                 
           re (a) - im (a) - 2*I*im(a)*re(a)            
--------------------------------------------------------
                     ___________________________________
/  2        2   \   /   4        4          2      2    
\im (a) + re (a)/*\/  im (a) + re (a) + 2*im (a)*re (a)

\frac{\left(\operatorname{re}{\left(a\right)}\right)^{2} - 2 i \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4}}}

(re(a)^2 - im(a)^2 - 2*i*im(a)*re(a))/((im(a)^2 + re(a)^2)*sqrt(im(a)^4 + re(a)^4 + 2*im(a)^2*re(a)^2))

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¿Cómo usar?

Expresiones idénticas

Expresiones con funciones

log(a^2*b^3)=0 la ecuación

Solución numérica:

Solución