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Ecuación x^4+2*x^2-8=0
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Ecuación x*(x^2+8*x+16)=5*(x+4)
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Ecuación -25-x=-17
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- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- -14*x+10*y=19
- -9*x+1*y=3
- -17*x+1*y=-11
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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^2+bx+c=0
- ax+b=cx+d
- ax^2+8*x-4*a-16=0
- ax^2+2x+3=0
- ax+8y=20
- ax
- ax^2+bx+c=0
- ax+b=cx+d
- ax^2+8*x-4*a-16=0
- ax^2+2x+3=0
- ax+8y=20
ax^2+ax+3=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Es la ecuación de la forma
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
$$b = a$$
$$c = 3$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{- a + \sqrt{a^{2} - 12 a}}{2 a}$$
$$x_{2} = \frac{- a - \sqrt{a^{2} - 12 a}}{2 a}$$
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)
o
$$x_{1} = \frac{- a + \sqrt{a^{2} - 12 a}}{2 a}$$
$$x_{2} = \frac{- a - \sqrt{a^{2} - 12 a}}{2 a}$$
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
$$a x^{2} + a x + 3 = 0$$
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
$$\left(a x^{2} + a x\right) + 3 = 0$$
de
$$a x^{2} + b x + c = 0$$
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
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -1$$
$$x_{1} x_{2} = \frac{3}{a}$$
$$\left(a x^{2} + a x\right) + 3 = 0$$
de
$$a x^{2} + b x + c = 0$$
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)$$
=
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| 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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/ 2 2 \ / 4 4 3 2 2 2 2 2
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))