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La ecuación:
Ecuación 3^x=27
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
Ecuación x(x^2+2x+1)=6(x+1)
Ecuación 4x+1=-3x+15
Expresar {x} en función de y en la ecuación:
-6*x-20*y=8
7*x-1*y=0
2*x-8*y=4
2*x-15*y=-1
Expresiones idénticas
ax^ dos +ax+ tres = cero
ax al cuadrado más ax más 3 es igual a 0
ax en el grado dos más ax más tres es igual a cero
ax2+ax+3=0
ax²+ax+3=0
ax en el grado 2+ax+3=0
ax^2+ax+3=O
Expresiones semejantes
ax^2+ax-3=0
ax^2-ax+3=0
Expresiones con funciones
ax
ax+b=c
ax+by+c=0
ax+b=cx+d
ax-b/a+b+bx+a/a-b=a^2+b^2/a^2-b^2
ax=2x+1
ax
ax+b=c
ax+by+c=0
ax+b=cx+d
ax-b/a+b+bx+a/a-b=a^2+b^2/a^2-b^2
ax=2x+1

ax^2+ax+3=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

   2              
a*x  + a*x + 3 = 0

\left(a x^{2} + a x\right) + 3 = 0

Simplificar

Solución detallada

Es la ecuación de la forma

a*x^2 + b*x + c = 0

La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:

x_{1} = \frac{\sqrt{D} - b}{2 a}

x_{2} = \frac{- \sqrt{D} - b}{2 a}

donde D = b^2 - 4*a*c es el discriminante.
Como

True

b = a

c = 3

, entonces

D = b^2 - 4 * a * c =

(a)^2 - 4 * (a) * (3) = a^2 - 12*a

La ecuación tiene dos raíces.

x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

x_{1} = \frac{- a + \sqrt{a^{2} - 12 a}}{2 a}

x_{2} = \frac{- a - \sqrt{a^{2} - 12 a}}{2 a}

Resolución de la ecuación paramétrica

Se da la ecuación con parámetro:

a x^{2} + a x + 3 = 0

Коэффициент при x равен

a

entonces son posibles los casos para a :

a < 0

a = 0

Consideremos todos los casos con detalles:
Con

a < 0

la ecuación será

- x^{2} - x + 3 = 0

su solución

x = - \frac{1}{2} + \frac{\sqrt{13}}{2}

x = - \frac{\sqrt{13}}{2} - \frac{1}{2}

Con

a = 0

la ecuación será

3 = 0

su solución
no hay soluciones

Teorema de Cardano-Vieta

reescribamos la ecuación

\left(a x^{2} + a x\right) + 3 = 0

a x^{2} + b x + c = 0

como ecuación cuadrática reducida

x^{2} + \frac{b x}{a} + \frac{c}{a} = 0

\frac{a x^{2} + a x + 3}{a} = 0

p x + q + x^{2} = 0

donde

p = \frac{b}{a}

p = 1

q = \frac{c}{a}

q = \frac{3}{a}

Fórmulas de Cardano-Vieta

x_{1} + x_{2} = - p

x_{1} x_{2} = q

x_{1} + x_{2} = -1

x_{1} x_{2} = \frac{3}{a}

Gráfica

Respuesta rápida [src]

       //             __________________________________________________________________________                                                                              \         /             __________________________________________________________________________                                                                              \      \   /             __________________________________________________________________________                                                                              \         /             __________________________________________________________________________                                                                              \      
       ||            /                                 2                                            /     /                                       2                         \\|         |            /                                 2                                            /     /                                       2                         \\|      |   |            /                                 2                                            /     /                                       2                         \\|         |            /                                 2                                            /     /                                       2                         \\|      
       ||         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||         |         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||      |   |         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||         |         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||      
       ||-im(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------||*re(a)   |-re(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------||*im(a)|   |-im(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------||*im(a)   |-re(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------||*re(a)
       |\                                                                                           \                                   2                                    //         \                                                                                           \                                   2                                    //      |   \                                                                                           \                                   2                                    //         \                                                                                           \                                   2                                    //      
x1 = I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
       |                                                                               /  2        2   \                                                                                                                                                               /  2        2   \                                                                             |                                                                                  /  2        2   \                                                                                                                                                               /  2        2   \                                                                             
       \                                                                             2*\im (a) + re (a)/                                                                                                                                                             2*\im (a) + re (a)/                                                                             /                                                                                2*\im (a) + re (a)/                                                                                                                                                             2*\im (a) + re (a)/

x_{1} = \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right)

       //    __________________________________________________________________________                                                                                      \         /    __________________________________________________________________________                                                                                      \      \   /    __________________________________________________________________________                                                                                      \         /    __________________________________________________________________________                                                                                      \      
       ||   /                                 2                                            /     /                                       2                         \\        |         |   /                                 2                                            /     /                                       2                         \\        |      |   |   /                                 2                                            /     /                                       2                         \\        |         |   /                                 2                                            /     /                                       2                         \\        |      
       ||4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |         |4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |      |   |4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |         |4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |      
       ||\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------| + re(a)|*im(a)   |\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------| + im(a)|*re(a)|   |\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------| + re(a)|*re(a)   |\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------| + im(a)|*im(a)
       |\                                                                                  \                                   2                                    /        /         \                                                                                  \                                   2                                    /        /      |   \                                                                                  \                                   2                                    /        /         \                                                                                  \                                   2                                    /        /      
x2 = I*|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
       |                                                                              /  2        2   \                                                                                                                                                              /  2        2   \                                                                             |                                                                                 /  2        2   \                                                                                                                                                              /  2        2   \                                                                             
       \                                                                            2*\im (a) + re (a)/                                                                                                                                                            2*\im (a) + re (a)/                                                                             /                                                                               2*\im (a) + re (a)/                                                                                                                                                            2*\im (a) + re (a)/

x_{2} = - \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{re}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(- \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{re}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right)

x2 = -((((re(a) - 12)*re(a) - im(a)^2)^2 + ((re(a) - 12)*im(a) + re(a)*im(a))^2)^(1/4)*sin(atan2((re(a) - 12)*im(a) + re(a)*im(a, (re(a) - 12)*re(a) - im(a)^2)/2) + im(a))*im(a)/(2*(re(a)^2 + im(a)^2)) - ((((re(a) - 12)*re(a) - im(a)^2)^2 + ((re(a) - 12)*im(a) + re(a)*im(a))^2)^(1/4)*cos(atan2((re(a) - 12)*im(a) + re(a)*im(a), (re(a) - 12)*re(a) - im(a)^2)/2) + re(a))*re(a)/(2*(re(a)^2 + im(a)^2)) + i*(-((((re(a) - 12)*re(a) - im(a)^2)^2 + ((re(a) - 12)*im(a) + re(a)*im(a))^2)^(1/4)*sin(atan2((re(a) - 12)*im(a) + re(a)*im(a), (re(a) - 12)*re(a) - im(a)^2)/2) + im(a))*re(a)/(2*(re(a)^2 + im(a)^2)) + ((((re(a) - 12)*re(a) - im(a)^2)^2 + ((re(a) - 12)*im(a) + re(a)*im(a))^2)^(1/4)*cos(atan2((re(a) - 12)*im(a) + re(a)*im(a), (re(a) - 12)*re(a) - im(a)^2)/2) + re(a))*im(a)/(2*(re(a)^2 + im(a)^2))))

Suma y producto de raíces [src]

suma

  //             __________________________________________________________________________                                                                              \         /             __________________________________________________________________________                                                                              \      \   /             __________________________________________________________________________                                                                              \         /             __________________________________________________________________________                                                                              \           //    __________________________________________________________________________                                                                                      \         /    __________________________________________________________________________                                                                                      \      \   /    __________________________________________________________________________                                                                                      \         /    __________________________________________________________________________                                                                                      \      
  ||            /                                 2                                            /     /                                       2                         \\|         |            /                                 2                                            /     /                                       2                         \\|      |   |            /                                 2                                            /     /                                       2                         \\|         |            /                                 2                                            /     /                                       2                         \\|           ||   /                                 2                                            /     /                                       2                         \\        |         |   /                                 2                                            /     /                                       2                         \\        |      |   |   /                                 2                                            /     /                                       2                         \\        |         |   /                                 2                                            /     /                                       2                         \\        |      
  ||         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||         |         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||      |   |         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||         |         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||           ||4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |         |4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |      |   |4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |         |4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |      
  ||-im(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------||*re(a)   |-re(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------||*im(a)|   |-im(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------||*im(a)   |-re(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------||*re(a)     ||\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------| + re(a)|*im(a)   |\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------| + im(a)|*re(a)|   |\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------| + re(a)|*re(a)   |\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------| + im(a)|*im(a)
  |\                                                                                           \                                   2                                    //         \                                                                                           \                                   2                                    //      |   \                                                                                           \                                   2                                    //         \                                                                                           \                                   2                                    //           |\                                                                                  \                                   2                                    /        /         \                                                                                  \                                   2                                    /        /      |   \                                                                                  \                                   2                                    /        /         \                                                                                  \                                   2                                    /        /      
I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + I*|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  |                                                                               /  2        2   \                                                                                                                                                               /  2        2   \                                                                             |                                                                                  /  2        2   \                                                                                                                                                               /  2        2   \                                                                                  |                                                                              /  2        2   \                                                                                                                                                              /  2        2   \                                                                             |                                                                                 /  2        2   \                                                                                                                                                              /  2        2   \                                                                             
  \                                                                             2*\im (a) + re (a)/                                                                                                                                                             2*\im (a) + re (a)/                                                                             /                                                                                2*\im (a) + re (a)/                                                                                                                                                             2*\im (a) + re (a)/                                                                                  \                                                                            2*\im (a) + re (a)/                                                                                                                                                            2*\im (a) + re (a)/                                                                             /                                                                               2*\im (a) + re (a)/                                                                                                                                                            2*\im (a) + re (a)/

\left(\frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right)\right) + \left(- \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{re}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(- \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{re}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right)\right)

  //             __________________________________________________________________________                                                                              \         /             __________________________________________________________________________                                                                              \      \     //    __________________________________________________________________________                                                                                      \         /    __________________________________________________________________________                                                                                      \      \   /             __________________________________________________________________________                                                                              \         /             __________________________________________________________________________                                                                              \         /    __________________________________________________________________________                                                                                      \         /    __________________________________________________________________________                                                                                      \      
  ||            /                                 2                                            /     /                                       2                         \\|         |            /                                 2                                            /     /                                       2                         \\|      |     ||   /                                 2                                            /     /                                       2                         \\        |         |   /                                 2                                            /     /                                       2                         \\        |      |   |            /                                 2                                            /     /                                       2                         \\|         |            /                                 2                                            /     /                                       2                         \\|         |   /                                 2                                            /     /                                       2                         \\        |         |   /                                 2                                            /     /                                       2                         \\        |      
  ||         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||         |         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||      |     ||4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |         |4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |      |   |         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||         |         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||         |4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |         |4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |      
  ||-im(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------||*re(a)   |-re(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------||*im(a)|     ||\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------| + re(a)|*im(a)   |\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------| + im(a)|*re(a)|   |-im(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------||*im(a)   |-re(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------||*re(a)   |\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------| + re(a)|*re(a)   |\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------| + im(a)|*im(a)
  |\                                                                                           \                                   2                                    //         \                                                                                           \                                   2                                    //      |     |\                                                                                  \                                   2                                    /        /         \                                                                                  \                                   2                                    /        /      |   \                                                                                           \                                   2                                    //         \                                                                                           \                                   2                                    //         \                                                                                  \                                   2                                    /        /         \                                                                                  \                                   2                                    /        /      
I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
  |                                                                               /  2        2   \                                                                                                                                                               /  2        2   \                                                                             |     |                                                                              /  2        2   \                                                                                                                                                              /  2        2   \                                                                             |                                                                                  /  2        2   \                                                                                                                                                               /  2        2   \                                                                                                                                                              /  2        2   \                                                                                                                                                              /  2        2   \                                                                             
  \                                                                             2*\im (a) + re (a)/                                                                                                                                                             2*\im (a) + re (a)/                                                                             /     \                                                                            2*\im (a) + re (a)/                                                                                                                                                            2*\im (a) + re (a)/                                                                             /                                                                                2*\im (a) + re (a)/                                                                                                                                                             2*\im (a) + re (a)/                                                                                                                                                            2*\im (a) + re (a)/                                                                                                                                                            2*\im (a) + re (a)/

\frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{re}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right) + i \left(- \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{re}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right)

producto

/  //             __________________________________________________________________________                                                                              \         /             __________________________________________________________________________                                                                              \      \   /             __________________________________________________________________________                                                                              \         /             __________________________________________________________________________                                                                              \      \ /  //    __________________________________________________________________________                                                                                      \         /    __________________________________________________________________________                                                                                      \      \   /    __________________________________________________________________________                                                                                      \         /    __________________________________________________________________________                                                                                      \      \
|  ||            /                                 2                                            /     /                                       2                         \\|         |            /                                 2                                            /     /                                       2                         \\|      |   |            /                                 2                                            /     /                                       2                         \\|         |            /                                 2                                            /     /                                       2                         \\|      | |  ||   /                                 2                                            /     /                                       2                         \\        |         |   /                                 2                                            /     /                                       2                         \\        |      |   |   /                                 2                                            /     /                                       2                         \\        |         |   /                                 2                                            /     /                                       2                         \\        |      |
|  ||         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||         |         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||      |   |         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||         |         4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/||      | |  ||4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |         |4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |      |   |4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |         |4 /  /    2                         \                                       2     |atan2\(-12 + re(a))*im(a) + im(a)*re(a), - im (a) + (-12 + re(a))*re(a)/|        |      |
|  ||-im(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------||*re(a)   |-re(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------||*im(a)|   |-im(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------||*im(a)   |-re(a) + \/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------||*re(a)| |  ||\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------| + re(a)|*im(a)   |\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------| + im(a)|*re(a)|   |\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *cos|------------------------------------------------------------------------| + re(a)|*re(a)   |\/   \- im (a) + (-12 + re(a))*re(a)/  + ((-12 + re(a))*im(a) + im(a)*re(a))  *sin|------------------------------------------------------------------------| + im(a)|*im(a)|
|  |\                                                                                           \                                   2                                    //         \                                                                                           \                                   2                                    //      |   \                                                                                           \                                   2                                    //         \                                                                                           \                                   2                                    //      | |  |\                                                                                  \                                   2                                    /        /         \                                                                                  \                                   2                                    /        /      |   \                                                                                  \                                   2                                    /        /         \                                                                                  \                                   2                                    /        /      |
|I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|I*|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
|  |                                                                               /  2        2   \                                                                                                                                                               /  2        2   \                                                                             |                                                                                  /  2        2   \                                                                                                                                                               /  2        2   \                                                                             | |  |                                                                              /  2        2   \                                                                                                                                                              /  2        2   \                                                                             |                                                                                 /  2        2   \                                                                                                                                                              /  2        2   \                                                                             |
\  \                                                                             2*\im (a) + re (a)/                                                                                                                                                             2*\im (a) + re (a)/                                                                             /                                                                                2*\im (a) + re (a)/                                                                                                                                                             2*\im (a) + re (a)/                                                                             / \  \                                                                            2*\im (a) + re (a)/                                                                                                                                                            2*\im (a) + re (a)/                                                                             /                                                                               2*\im (a) + re (a)/                                                                                                                                                            2*\im (a) + re (a)/                                                                             /

\left(\frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(\frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \operatorname{re}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right)\right) \left(- \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} - \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{re}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + i \left(- \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{im}{\left(a\right)}\right) \operatorname{re}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)} + \frac{\left(\sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 12\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \operatorname{re}{\left(a\right)}\right) \operatorname{im}{\left(a\right)}}{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)}\right)\right)

 /                                                           ___________________________________________________________________________________________             ___________________________________________________________________________________________                                  ___________________________________________________________________________________________                              _________________    __________________________________             _________________    __________________________________             _________________    __________________________________    ___________________________________________________________________________________________         _________________    __________________________________                 _________________    __________________________________    ___________________________________________________________________________________________      \ 
 |  4        4           3            2            2        /   4        4           3            2            2           2                2      2       2        /   4        4           3            2            2           2                2      2       2           2                 /   4        4           3            2            2           2                2      2                 2      2        /   2        2       /         2        2                  2        /   2        2       /         2        2                  2        /   2        2       /         2        2                  /   4        4           3            2            2           2                2      2            /   2        2       /         2        2                             4 /   2        2     4 /         2        2                4 /   4        4           3            2            2           2                2      2          | 
-\im (a) + re (a) - 24*re (a) + 144*im (a) + 144*re (a) - \/  im (a) + re (a) - 24*re (a) + 144*im (a) + 144*re (a) - 24*im (a)*re(a) + 2*im (a)*re (a) *im (a) - \/  im (a) + re (a) - 24*re (a) + 144*im (a) + 144*re (a) - 24*im (a)*re(a) + 2*im (a)*re (a) *re (a) - 24*im (a)*re(a) - 12*\/  im (a) + re (a) - 24*re (a) + 144*im (a) + 144*re (a) - 24*im (a)*re(a) + 2*im (a)*re (a) *re(a) + 2*im (a)*re (a) + \/  im (a) + re (a) *\/  144 + im (a) + re (a) - 24*re(a) *im (a) + \/  im (a) + re (a) *\/  144 + im (a) + re (a) - 24*re(a) *re (a) - \/  im (a) + re (a) *\/  144 + im (a) + re (a) - 24*re(a) *\/  im (a) + re (a) - 24*re (a) + 144*im (a) + 144*re (a) - 24*im (a)*re(a) + 2*im (a)*re (a)  - 12*\/  im (a) + re (a) *\/  144 + im (a) + re (a) - 24*re(a) *re(a) + 24*I*\/  im (a) + re (a) *\/  144 + im (a) + re (a) - 24*re(a) *\/  im (a) + re (a) - 24*re (a) + 144*im (a) + 144*re (a) - 24*im (a)*re(a) + 2*im (a)*re (a) *im(a)/ 
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                                                                                                                                                                                                                                                                                                                                                                                                                           8*\im (a) + re (a)/*\/  im (a) + re (a) - 24*re (a) + 144*im (a) + 144*re (a) - 24*im (a)*re(a) + 2*im (a)*re (a)

- \frac{24 i \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{2} - 24 \operatorname{re}{\left(a\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{2} + 144} \sqrt[4]{\left(\operatorname{re}{\left(a\right)}\right)^{4} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{3} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 144 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 24 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 144 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \operatorname{im}{\left(a\right)} - \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} - 24 \operatorname{re}{\left(a\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{2} + 144} \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{4} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{3} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 144 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 24 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 144 \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} - 24 \operatorname{re}{\left(a\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{2} + 144} \left(\operatorname{re}{\left(a\right)}\right)^{2} - 12 \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} - 24 \operatorname{re}{\left(a\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{2} + 144} \operatorname{re}{\left(a\right)} + \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{2} - 24 \operatorname{re}{\left(a\right)} + \left(\operatorname{im}{\left(a\right)}\right)^{2} + 144} \left(\operatorname{im}{\left(a\right)}\right)^{2} - \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{4} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{3} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 144 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 24 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 144 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(a\right)}\right)^{2} - 12 \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{4} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{3} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 144 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 24 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 144 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \operatorname{re}{\left(a\right)} - \sqrt{\left(\operatorname{re}{\left(a\right)}\right)^{4} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{3} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 144 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 24 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 144 \left(\operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(a\right)}\right)^{4} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{3} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 144 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 24 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 144 \left(\operatorname{im}{\left(a\right)}\right)^{2}}{8 \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} - 24 \left(\operatorname{re}{\left(a\right)}\right)^{3} + 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 144 \left(\operatorname{re}{\left(a\right)}\right)^{2} - 24 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 144 \left(\operatorname{im}{\left(a\right)}\right)^{2}}}

-(im(a)^4 + re(a)^4 - 24*re(a)^3 + 144*im(a)^2 + 144*re(a)^2 - sqrt(im(a)^4 + re(a)^4 - 24*re(a)^3 + 144*im(a)^2 + 144*re(a)^2 - 24*im(a)^2*re(a) + 2*im(a)^2*re(a)^2)*im(a)^2 - sqrt(im(a)^4 + re(a)^4 - 24*re(a)^3 + 144*im(a)^2 + 144*re(a)^2 - 24*im(a)^2*re(a) + 2*im(a)^2*re(a)^2)*re(a)^2 - 24*im(a)^2*re(a) - 12*sqrt(im(a)^4 + re(a)^4 - 24*re(a)^3 + 144*im(a)^2 + 144*re(a)^2 - 24*im(a)^2*re(a) + 2*im(a)^2*re(a)^2)*re(a) + 2*im(a)^2*re(a)^2 + sqrt(im(a)^2 + re(a)^2)*sqrt(144 + im(a)^2 + re(a)^2 - 24*re(a))*im(a)^2 + sqrt(im(a)^2 + re(a)^2)*sqrt(144 + im(a)^2 + re(a)^2 - 24*re(a))*re(a)^2 - sqrt(im(a)^2 + re(a)^2)*sqrt(144 + im(a)^2 + re(a)^2 - 24*re(a))*sqrt(im(a)^4 + re(a)^4 - 24*re(a)^3 + 144*im(a)^2 + 144*re(a)^2 - 24*im(a)^2*re(a) + 2*im(a)^2*re(a)^2) - 12*sqrt(im(a)^2 + re(a)^2)*sqrt(144 + im(a)^2 + re(a)^2 - 24*re(a))*re(a) + 24*i*(im(a)^2 + re(a)^2)^(1/4)*(144 + im(a)^2 + re(a)^2 - 24*re(a))^(1/4)*(im(a)^4 + re(a)^4 - 24*re(a)^3 + 144*im(a)^2 + 144*re(a)^2 - 24*im(a)^2*re(a) + 2*im(a)^2*re(a)^2)^(1/4)*im(a))/(8*(im(a)^2 + re(a)^2)*sqrt(im(a)^4 + re(a)^4 - 24*re(a)^3 + 144*im(a)^2 + 144*re(a)^2 - 24*im(a)^2*re(a) + 2*im(a)^2*re(a)^2))

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ax^2+ax+3=0 la ecuación

Solución numérica:

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