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- La ecuación:
-
Ecuación x+9=0
-
Ecuación 2x^2+7x-9=0
-
Ecuación 5*x^2+9*x=0
-
Ecuación 3x^2=2x+x^3
- Expresar {x} en función de y en la ecuación:
- -6*x+11*y=-5
- -15*x+7*y=1
- -11*x-11*y=4
- -14*x+4*y=-16
- Factorizar el polinomio:
- a^2-1
-
Expresiones idénticas
- Sqrt(x^ dos - uno)*sqrt(y^ dos - uno)=a^ dos - uno
- Sqrt(x al cuadrado menos 1) multiplicar por raíz cuadrada de (y al cuadrado menos 1) es igual a a al cuadrado menos 1
- Sqrt(x en el grado dos menos uno) multiplicar por raíz cuadrada de (y en el grado dos menos uno) es igual a a en el grado dos menos uno
- Sqrt(x^2-1)*√(y^2-1)=a^2-1
- Sqrt(x2-1)*sqrt(y2-1)=a2-1
- Sqrtx2-1*sqrty2-1=a2-1
- Sqrt(x²-1)*sqrt(y²-1)=a²-1
- Sqrt(x en el grado 2-1)*sqrt(y en el grado 2-1)=a en el grado 2-1
- Sqrt(x^2-1)sqrt(y^2-1)=a^2-1
- Sqrt(x2-1)sqrt(y2-1)=a2-1
- Sqrtx2-1sqrty2-1=a2-1
- Sqrtx^2-1sqrty^2-1=a^2-1
-
Expresiones semejantes
- Sqrt(x^2-1)*sqrt(y^2+1)=a^2-1
- Sqrt(x^2+1)*sqrt(y^2-1)=a^2-1
- Sqrt(x^2-1)*sqrt(y^2-1)=a^2+1
-
Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(7-8×x+sqr(x))+sqrt(sqr(x)-8×x-5)=-sqr(x)+8×x+15
- sqrt((x)/(x-2))+sqrt((x-2)/(x))=5/2
- sqrt(7+3x)-sqrt(5-4x)+1=0
- sqrt((1-a)^10)=(1-a)^5
- sqrt2x^2+2x-1=-x-1
Sqrt(x^2-1)*sqrt(y^2-1)=a^2-1 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
________ ________ / 2 / 2 2 \/ x - 1 *\/ y - 1 = a - 1
$$\sqrt{x^{2} - 1} \sqrt{y^{2} - 1} = a^{2} - 1$$
Solución detallada
Tenemos la ecuación
$$\sqrt{x^{2} - 1} \sqrt{y^{2} - 1} = a^{2} - 1$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$\sqrt{x^{2} - 1} \sqrt{y^{2} - 1} = a^{2} - 1$$
Elevemos las dos partes de la ecuación a la potencia 2
$$\left(x^{2} - 1\right) \left(y^{2} - 1\right) = \left(a^{2} - 1\right)^{2}$$
$$\left(x^{2} - 1\right) \left(y^{2} - 1\right) = a^{4} - 2 a^{2} + 1$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- a^{4} + 2 a^{2} + \left(x^{2} - 1\right) \left(y^{2} - 1\right) - 1 = 0$$
Abramos la expresión en la ecuación
$$- a^{4} + 2 a^{2} + \left(x^{2} - 1\right) \left(y^{2} - 1\right) - 1 = 0$$
Obtenemos la ecuación cuadrática
$$- a^{4} + 2 a^{2} + x^{2} y^{2} - x^{2} - y^{2} = 0$$
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
$$a = y^{2} - 1$$
$$b = 0$$
$$c = - a^{4} + 2 a^{2} - y^{2}$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{\sqrt{- \left(4 y^{2} - 4\right) \left(- a^{4} + 2 a^{2} - y^{2}\right)}}{2 y^{2} - 2}$$
$$x_{2} = - \frac{\sqrt{- \left(4 y^{2} - 4\right) \left(- a^{4} + 2 a^{2} - y^{2}\right)}}{2 y^{2} - 2}$$
$$\sqrt{x^{2} - 1} \sqrt{y^{2} - 1} = a^{2} - 1$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$\sqrt{x^{2} - 1} \sqrt{y^{2} - 1} = a^{2} - 1$$
Elevemos las dos partes de la ecuación a la potencia 2
$$\left(x^{2} - 1\right) \left(y^{2} - 1\right) = \left(a^{2} - 1\right)^{2}$$
$$\left(x^{2} - 1\right) \left(y^{2} - 1\right) = a^{4} - 2 a^{2} + 1$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- a^{4} + 2 a^{2} + \left(x^{2} - 1\right) \left(y^{2} - 1\right) - 1 = 0$$
Abramos la expresión en la ecuación
$$- a^{4} + 2 a^{2} + \left(x^{2} - 1\right) \left(y^{2} - 1\right) - 1 = 0$$
Obtenemos la ecuación cuadrática
$$- a^{4} + 2 a^{2} + x^{2} y^{2} - x^{2} - y^{2} = 0$$
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
$$a = y^{2} - 1$$
$$b = 0$$
$$c = - a^{4} + 2 a^{2} - y^{2}$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-1 + y^2) * (-a^4 - y^2 + 2*a^2) = -(-4 + 4*y^2)*(-a^4 - y^2 + 2*a^2)
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{\sqrt{- \left(4 y^{2} - 4\right) \left(- a^{4} + 2 a^{2} - y^{2}\right)}}{2 y^{2} - 2}$$
$$x_{2} = - \frac{\sqrt{- \left(4 y^{2} - 4\right) \left(- a^{4} + 2 a^{2} - y^{2}\right)}}{2 y^{2} - 2}$$
Gráfica
Respuesta rápida
[src]
/ // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ / 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \\ / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ / 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \\
| |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y) \-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)|| | |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y) \-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)||
_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------, -------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------|| _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------, -------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------||
/ 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||
/ // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||
/ |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)| |\-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)| | \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)| |\-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)| | \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /|
x1 = - / |------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------| + |-------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I* / |------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------| + |-------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
/ | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 /
4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 |
\/ \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /
$$x_{1} = - i \sqrt[4]{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)}$$
/ // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ / 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \\ / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ / 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \\
| |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y) \-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)|| | |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y) \-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)||
_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------, -------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------|| _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------, -------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------||
/ 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||
/ // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||
/ |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)| |\-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)| | \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)| |\-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)| | \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /|
x2 = / |------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------| + |-------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I* / |------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------| + |-------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
/ | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 /
4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 |
\/ \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /
$$x_{2} = i \sqrt[4]{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)}$$
x2 = i*(((re(y)^2 - im(y)^2 - 1)*(4*re(a)^3*im(a) - 4*re(a)*im(a)^3 - 4*re(a)*im(a) + 2*re(y)*im(y))/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2) - 2*(re(a)^4 - 6*re(a)^2*im(a)^2 - 2*re(a)^2 + re(y)^2 + im(a)^4 + 2*im(a)^2 - im(y)^2)*re(y)*im(y)/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2))^2 + ((re(y)^2 - im(y)^2 - 1)*(re(a)^4 - 6*re(a)^2*im(a)^2 - 2*re(a)^2 + re(y)^2 + im(a)^4 + 2*im(a)^2 - im(y)^2)/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2) + 2*(4*re(a)^3*im(a) - 4*re(a)*im(a)^3 - 4*re(a)*im(a) + 2*re(y)*im(y))*re(y)*im(y)/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2))^2)^(1/4)*sin(atan2((re(y)^2 - im(y)^2 - 1)*(4*re(a)^3*im(a) - 4*re(a)*im(a)^3 - 4*re(a)*im(a) + 2*re(y)*im(y))/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2) - 2*(re(a)^4 - 6*re(a)^2*im(a)^2 - 2*re(a)^2 + re(y)^2 + im(a)^4 + 2*im(a)^2 - im(y)^2)*re(y)*im(y)/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2, (re(y)^2 - im(y)^2 - 1)*(re(a)^4 - 6*re(a)^2*im(a)^2 - 2*re(a)^2 + re(y)^2 + im(a)^4 + 2*im(a)^2 - im(y)^2)/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2) + 2*(4*re(a)^3*im(a) - 4*re(a)*im(a)^3 - 4*re(a)*im(a) + 2*re(y)*im(y))*re(y)*im(y)/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2))/2) + (((re(y)^2 - im(y)^2 - 1)*(4*re(a)^3*im(a) - 4*re(a)*im(a)^3 - 4*re(a)*im(a) + 2*re(y)*im(y))/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2) - 2*(re(a)^4 - 6*re(a)^2*im(a)^2 - 2*re(a)^2 + re(y)^2 + im(a)^4 + 2*im(a)^2 - im(y)^2)*re(y)*im(y)/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2))^2 + ((re(y)^2 - im(y)^2 - 1)*(re(a)^4 - 6*re(a)^2*im(a)^2 - 2*re(a)^2 + re(y)^2 + im(a)^4 + 2*im(a)^2 - im(y)^2)/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2) + 2*(4*re(a)^3*im(a) - 4*re(a)*im(a)^3 - 4*re(a)*im(a) + 2*re(y)*im(y))*re(y)*im(y)/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2))^2)^(1/4)*cos(atan2((re(y)^2 - im(y)^2 - 1)*(4*re(a)^3*im(a) - 4*re(a)*im(a)^3 - 4*re(a)*im(a) + 2*re(y)*im(y))/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2) - 2*(re(a)^4 - 6*re(a)^2*im(a)^2 - 2*re(a)^2 + re(y)^2 + im(a)^4 + 2*im(a)^2 - im(y)^2)*re(y)*im(y)/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2), (re(y)^2 - im(y)^2 - 1)*(re(a)^4 - 6*re(a)^2*im(a)^2 - 2*re(a)^2 + re(y)^2 + im(a)^4 + 2*im(a)^2 - im(y)^2)/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2) + 2*(4*re(a)^3*im(a) - 4*re(a)*im(a)^3 - 4*re(a)*im(a) + 2*re(y)*im(y))*re(y)*im(y)/((re(y)^2 - im(y)^2 - 1)^2 + 4*re(y)^2*im(y)^2))/2))
Suma y producto de raíces
[src]
suma
/ // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ / 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \\ / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ / 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \\ / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ / 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \\ / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ / 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \\
| |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y) \-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)|| | |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y) \-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)|| | |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y) \-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)|| | |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y) \-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)||
_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------, -------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------|| _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------, -------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------|| _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------, -------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------|| _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------, -------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------||
/ 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||
/ // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||
/ |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)| |\-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)| | \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)| |\-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)| | \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)| |\-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)| | \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)| |\-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)| | \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /|
- / |------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------| + |-------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I* / |------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------| + |-------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + / |------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------| + |-------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I* / |------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------| + |-------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
/ | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 /
4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 |
\/ \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /
$$\left(- i \sqrt[4]{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ / 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \\ / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ / 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \\\ / / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ / 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \\ / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ / 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \\\ | | |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y) \-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)|| | |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y) \-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)||| | | |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y) \-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)|| | |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y) \-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)||| | _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------, -------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------|| _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------, -------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------||| | _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------, -------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------|| _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ |atan2|------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------, -------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------||| | / 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||| | / 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||| | / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||| | / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 || / // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ | | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 ||| | / |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)| |\-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)| | \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)| |\-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)| | \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /|| | / |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)| |\-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)| | \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /| / |\-1 + re (y) - im (y)/*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/ 2*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)| |\-1 + re (y) - im (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ 2*\- 4*im (a)*re(a) - 4*im(a)*re(a) + 2*im(y)*re(y) + 4*re (a)*im(a)/*im(y)*re(y)| | \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) /|| |- / |------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------| + |-------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| - I* / |------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------| + |-------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------||*| / |------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------| + |-------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------| *cos|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I* / |------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------| + |-------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------| *sin|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| | / | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 /| | / | 2 2 | | 2 2 | \ 2 / / | 2 2 | | 2 2 | \ 2 /| | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | | |4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | 4 / | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | | \ \/ \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / / \\/ \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \/ \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \-1 + re (y) - im (y)/ + 4*im (y)*re (y) \-1 + re (y) - im (y)/ + 4*im (y)*re (y) / /
$$\left(- i \sqrt[4]{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2} + \left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},\frac{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(4 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 4 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 4 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}{2} \right)}\right)$$
=
/ // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ \
|-2*\\1 + im (y) - re (y)/*\im(y)*re(y) - 2*im (a)*re(a) - 2*im(a)*re(a) + 2*re (a)*im(a)/ + \im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)/ -\\1 + im (y) - re (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ - 4*\im(y)*re(y) - 2*im (a)*re(a) - 2*im(a)*re(a) + 2*re (a)*im(a)/*im(y)*re(y)/ |
I*atan2|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------, -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ | 2 2 |
/ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 |
/ // 2 2 \ / 4 4 2 2 2 2 2 2 \ / 3 3 \ \ // 2 2 \ / 3 3 \ / 4 4 2 2 2 2 2 2 \ \ \ \1 + im (y) - re (y)/ + 4*im (y)*re (y) \1 + im (y) - re (y)/ + 4*im (y)*re (y) /
-\/ \\1 + im (y) - re (y)/*\im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/ - 4*\im(y)*re(y) - 2*im (a)*re(a) - 2*im(a)*re(a) + 2*re (a)*im(a)/*im(y)*re(y)/ + 4*\\1 + im (y) - re (y)/*\im(y)*re(y) - 2*im (a)*re(a) - 2*im(a)*re(a) + 2*re (a)*im(a)/ + \im (a) + re (a) + re (y) - im (y) - 2*re (a) + 2*im (a) - 6*im (a)*re (a)/*im(y)*re(y)/ *e
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2
/ 2 2 \ 2 2
\1 + im (y) - re (y)/ + 4*im (y)*re (y)
$$- \frac{\sqrt{4 \left(\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(2 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 2 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) + \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2} + \left(\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) - 4 \left(2 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 2 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(- \frac{2 \left(\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(2 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 2 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) + \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right)}{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}},- \frac{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right) \left(\left(\operatorname{re}{\left(a\right)}\right)^{4} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{4} + 2 \left(\operatorname{im}{\left(a\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2}\right) - 4 \left(2 \left(\operatorname{re}{\left(a\right)}\right)^{3} \operatorname{im}{\left(a\right)} - 2 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \right)}}}{\left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}$$
-sqrt(((1 + im(y)^2 - re(y)^2)*(im(a)^4 + re(a)^4 + re(y)^2 - im(y)^2 - 2*re(a)^2 + 2*im(a)^2 - 6*im(a)^2*re(a)^2) - 4*(im(y)*re(y) - 2*im(a)^3*re(a) - 2*im(a)*re(a) + 2*re(a)^3*im(a))*im(y)*re(y))^2 + 4*((1 + im(y)^2 - re(y)^2)*(im(y)*re(y) - 2*im(a)^3*re(a) - 2*im(a)*re(a) + 2*re(a)^3*im(a)) + (im(a)^4 + re(a)^4 + re(y)^2 - im(y)^2 - 2*re(a)^2 + 2*im(a)^2 - 6*im(a)^2*re(a)^2)*im(y)*re(y))^2)*exp(i*atan2(-2*((1 + im(y)^2 - re(y)^2)*(im(y)*re(y) - 2*im(a)^3*re(a) - 2*im(a)*re(a) + 2*re(a)^3*im(a)) + (im(a)^4 + re(a)^4 + re(y)^2 - im(y)^2 - 2*re(a)^2 + 2*im(a)^2 - 6*im(a)^2*re(a)^2)*im(y)*re(y))/((1 + im(y)^2 - re(y)^2)^2 + 4*im(y)^2*re(y)^2), -((1 + im(y)^2 - re(y)^2)*(im(a)^4 + re(a)^4 + re(y)^2 - im(y)^2 - 2*re(a)^2 + 2*im(a)^2 - 6*im(a)^2*re(a)^2) - 4*(im(y)*re(y) - 2*im(a)^3*re(a) - 2*im(a)*re(a) + 2*re(a)^3*im(a))*im(y)*re(y))/((1 + im(y)^2 - re(y)^2)^2 + 4*im(y)^2*re(y)^2)))/((1 + im(y)^2 - re(y)^2)^2 + 4*im(y)^2*re(y)^2)