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- La ecuación:
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Ecuación 2*x^2+6*x+9=0
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- Expresar {x} en función de y en la ecuación:
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Expresiones idénticas
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- ax en el grado dos más (3a más dos)y en el grado dos más cuatro axy menos dos ax más (4 menos 6a)y más 2 es igual a cero
- ax2+(3a+2)y2+4axy-2ax+(4-6a)y+2=0
- ax2+3a+2y2+4axy-2ax+4-6ay+2=0
- ax²+(3a+2)y²+4axy-2ax+(4-6a)y+2=0
- ax en el grado 2+(3a+2)y en el grado 2+4axy-2ax+(4-6a)y+2=0
- ax^2+3a+2y^2+4axy-2ax+4-6ay+2=0
- ax^2+(3a+2)y^2+4axy-2ax+(4-6a)y+2=O
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Expresiones semejantes
- ax^2+(3a+2)y^2+4axy+2ax+(4-6a)y+2=0
- ax^2+(3a-2)y^2+4axy-2ax+(4-6a)y+2=0
- ax^2+(3a+2)y^2+4axy-2ax-(4-6a)y+2=0
- ax^2+(3a+2)y^2+4axy-2ax+(4-6a)y-2=0
- ax^2+(3a+2)y^2+4axy-2ax+(4+6a)y+2=0
- ax^2+(3a+2)y^2-4axy-2ax+(4-6a)y+2=0
- ax^2-(3a+2)y^2+4axy-2ax+(4-6a)y+2=0
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Expresiones con funciones
- ax
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- Ax^4Px-4Px-2=42
- ax+2x+6=0
- ax+b-b=cx+d-b
- ax=2x+1
ax^2+(3a+2)y^2+4axy-2ax+(4-6a)y+2=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 a*x + (3*a + 2)*y + 4*a*x*y - 2*a*x + (4 - 6*a)*y + 2 = 0
$$\left(y \left(4 - 6 a\right) + \left(- 2 a x + \left(y 4 a x + \left(a x^{2} + y^{2} \left(3 a + 2\right)\right)\right)\right)\right) + 2 = 0$$
Solución detallada
Abramos la expresión en la ecuación
$$\left(y \left(4 - 6 a\right) + \left(- 2 a x + \left(y 4 a x + \left(a x^{2} + y^{2} \left(3 a + 2\right)\right)\right)\right)\right) + 2 = 0$$
Obtenemos la ecuación cuadrática
$$a x^{2} + 3 a y^{2} - 6 a y - 2 a x + 2 y^{2} + y 4 a x + 4 y + 2 = 0$$
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
$$b = 4 a y - 2 a$$
$$c = 3 a y^{2} - 6 a y + 2 y^{2} + 4 y + 2$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{- 4 a y + 2 a + \sqrt{- 4 a \left(3 a y^{2} - 6 a y + 2 y^{2} + 4 y + 2\right) + \left(4 a y - 2 a\right)^{2}}}{2 a}$$
$$x_{2} = \frac{- 4 a y + 2 a - \sqrt{- 4 a \left(3 a y^{2} - 6 a y + 2 y^{2} + 4 y + 2\right) + \left(4 a y - 2 a\right)^{2}}}{2 a}$$
$$\left(y \left(4 - 6 a\right) + \left(- 2 a x + \left(y 4 a x + \left(a x^{2} + y^{2} \left(3 a + 2\right)\right)\right)\right)\right) + 2 = 0$$
Obtenemos la ecuación cuadrática
$$a x^{2} + 3 a y^{2} - 6 a y - 2 a x + 2 y^{2} + y 4 a x + 4 y + 2 = 0$$
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
True
$$b = 4 a y - 2 a$$
$$c = 3 a y^{2} - 6 a y + 2 y^{2} + 4 y + 2$$
, entonces
D = b^2 - 4 * a * c =
(-2*a + 4*a*y)^2 - 4 * (a) * (2 + 2*y^2 + 4*y - 6*a*y + 3*a*y^2) = (-2*a + 4*a*y)^2 - 4*a*(2 + 2*y^2 + 4*y - 6*a*y + 3*a*y^2)
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{- 4 a y + 2 a + \sqrt{- 4 a \left(3 a y^{2} - 6 a y + 2 y^{2} + 4 y + 2\right) + \left(4 a y - 2 a\right)^{2}}}{2 a}$$
$$x_{2} = \frac{- 4 a y + 2 a - \sqrt{- 4 a \left(3 a y^{2} - 6 a y + 2 y^{2} + 4 y + 2\right) + \left(4 a y - 2 a\right)^{2}}}{2 a}$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$a x^{2} + 4 a x y - 2 a x + y^{2} \left(3 a + 2\right) + y \left(4 - 6 a\right) + 2 = 0$$
Коэффициент при x равен
$$a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$- x^{2} - 4 x y + 2 x - y^{2} + 10 y + 2 = 0$$
su solución
$$x = - 2 y - \sqrt{3} \left(y + 1\right) + 1$$
$$x = - 2 y + \sqrt{3} \left(y + 1\right) + 1$$
Con
$$a = 0$$
la ecuación será
$$2 y^{2} + 4 y + 2 = 0$$
su solución
$$a x^{2} + 4 a x y - 2 a x + y^{2} \left(3 a + 2\right) + y \left(4 - 6 a\right) + 2 = 0$$
Коэффициент при x равен
$$a$$
entonces son posibles los casos para a :
$$a < 0$$
$$a = 0$$
Consideremos todos los casos con detalles:
Con
$$a < 0$$
la ecuación será
$$- x^{2} - 4 x y + 2 x - y^{2} + 10 y + 2 = 0$$
su solución
$$x = - 2 y - \sqrt{3} \left(y + 1\right) + 1$$
$$x = - 2 y + \sqrt{3} \left(y + 1\right) + 1$$
Con
$$a = 0$$
la ecuación será
$$2 y^{2} + 4 y + 2 = 0$$
su solución
Teorema de Cardano-Vieta
reescribamos la ecuación
$$\left(y \left(4 - 6 a\right) + \left(- 2 a x + \left(y 4 a x + \left(a x^{2} + y^{2} \left(3 a + 2\right)\right)\right)\right)\right) + 2 = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{a x^{2} + 4 a x y - 2 a x + y^{2} \left(3 a + 2\right) + y \left(4 - 6 a\right) + 2}{a} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{4 a y - 2 a}{a}$$
$$q = \frac{c}{a}$$
$$q = \frac{y^{2} \left(3 a + 2\right) - y \left(6 a - 4\right) + 2}{a}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{4 a y - 2 a}{a}$$
$$x_{1} x_{2} = \frac{y^{2} \left(3 a + 2\right) - y \left(6 a - 4\right) + 2}{a}$$
$$\left(y \left(4 - 6 a\right) + \left(- 2 a x + \left(y 4 a x + \left(a x^{2} + y^{2} \left(3 a + 2\right)\right)\right)\right)\right) + 2 = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{a x^{2} + 4 a x y - 2 a x + y^{2} \left(3 a + 2\right) + y \left(4 - 6 a\right) + 2}{a} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = \frac{4 a y - 2 a}{a}$$
$$q = \frac{c}{a}$$
$$q = \frac{y^{2} \left(3 a + 2\right) - y \left(6 a - 4\right) + 2}{a}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{4 a y - 2 a}{a}$$
$$x_{1} x_{2} = \frac{y^{2} \left(3 a + 2\right) - y \left(6 a - 4\right) + 2}{a}$$
Gráfica
Respuesta rápida
[src]
// ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ \ / ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \
|| / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\| | | / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\|
|| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/||
||(1 - 2*re(y))*im(a) - 2*im(y)*re(a) - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*re(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------||*im(a)| |(1 - 2*re(y))*im(a) - 2*im(y)*re(a) - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*im(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------||*re(a)
|\ \ 2 / \ 2 / / \ \ 2 / \ 2 // | \ \ 2 / \ 2 / / \ \ 2 / \ 2 //
x1 = I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 2 2 2 | 2 2 2 2
\ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$x_{1} = i \left(- \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
// ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ \ / ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \
|| / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\| | | / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\|
|| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/||
||(1 - 2*re(y))*im(a) - 2*im(y)*re(a) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*re(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------||*im(a)| |(1 - 2*re(y))*im(a) - 2*im(y)*re(a) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*im(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------||*re(a)
|\ \ 2 / \ 2 / / \ \ 2 / \ 2 // | \ \ 2 / \ 2 / / \ \ 2 / \ 2 //
x2 = I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 2 2 2 | 2 2 2 2
\ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$x_{2} = i \left(- \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
x2 = i*(-((1 - 2*re(y))*re(a) + (((re(a) - 2)*re(a) - im(a)^2)^2 + ((re(a) - 2)*im(a) + re(a)*im(a))^2)^(1/4)*(re(y) + 1)*cos(atan2((re(a) - 2)*im(a) + re(a)*im(a, (re(a) - 2)*re(a) - im(a)^2)/2) - (((re(a) - 2)*re(a) - im(a)^2)^2 + ((re(a) - 2)*im(a) + re(a)*im(a))^2)^(1/4)*sin(atan2((re(a) - 2)*im(a) + re(a)*im(a), (re(a) - 2)*re(a) - im(a)^2)/2)*im(y) + 2*im(a)*im(y))*im(a)/(re(a)^2 + im(a)^2) + ((1 - 2*re(y))*im(a) + (((re(a) - 2)*re(a) - im(a)^2)^2 + ((re(a) - 2)*im(a) + re(a)*im(a))^2)^(1/4)*(re(y) + 1)*sin(atan2((re(a) - 2)*im(a) + re(a)*im(a), (re(a) - 2)*re(a) - im(a)^2)/2) + (((re(a) - 2)*re(a) - im(a)^2)^2 + ((re(a) - 2)*im(a) + re(a)*im(a))^2)^(1/4)*cos(atan2((re(a) - 2)*im(a) + re(a)*im(a), (re(a) - 2)*re(a) - im(a)^2)/2)*im(y) - 2*re(a)*im(y))*re(a)/(re(a)^2 + im(a)^2)) + ((1 - 2*re(y))*re(a) + (((re(a) - 2)*re(a) - im(a)^2)^2 + ((re(a) - 2)*im(a) + re(a)*im(a))^2)^(1/4)*(re(y) + 1)*cos(atan2((re(a) - 2)*im(a) + re(a)*im(a), (re(a) - 2)*re(a) - im(a)^2)/2) - (((re(a) - 2)*re(a) - im(a)^2)^2 + ((re(a) - 2)*im(a) + re(a)*im(a))^2)^(1/4)*sin(atan2((re(a) - 2)*im(a) + re(a)*im(a), (re(a) - 2)*re(a) - im(a)^2)/2)*im(y) + 2*im(a)*im(y))*re(a)/(re(a)^2 + im(a)^2) + ((1 - 2*re(y))*im(a) + (((re(a) - 2)*re(a) - im(a)^2)^2 + ((re(a) - 2)*im(a) + re(a)*im(a))^2)^(1/4)*(re(y) + 1)*sin(atan2((re(a) - 2)*im(a) + re(a)*im(a), (re(a) - 2)*re(a) - im(a)^2)/2) + (((re(a) - 2)*re(a) - im(a)^2)^2 + ((re(a) - 2)*im(a) + re(a)*im(a))^2)^(1/4)*cos(atan2((re(a) - 2)*im(a) + re(a)*im(a), (re(a) - 2)*re(a) - im(a)^2)/2)*im(y) - 2*re(a)*im(y))*im(a)/(re(a)^2 + im(a)^2))
Suma y producto de raíces
[src]
suma
// ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ \ / ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ // ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ \ / ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ || / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\| | | / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\| || / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\| | | / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\| || 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| || 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| ||(1 - 2*re(y))*im(a) - 2*im(y)*re(a) - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*re(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------||*im(a)| |(1 - 2*re(y))*im(a) - 2*im(y)*re(a) - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*im(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------||*re(a) ||(1 - 2*re(y))*im(a) - 2*im(y)*re(a) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*re(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------||*im(a)| |(1 - 2*re(y))*im(a) - 2*im(y)*re(a) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*im(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------||*re(a) |\ \ 2 / \ 2 / / \ \ 2 / \ 2 // | \ \ 2 / \ 2 / / \ \ 2 / \ 2 // |\ \ 2 / \ 2 / / \ \ 2 / \ 2 // | \ \ 2 / \ 2 / / \ \ 2 / \ 2 // I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 2 2 2 2 | 2 2 2 2 | 2 2 2 2 | 2 2 2 2 \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a) \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a)
$$\left(i \left(- \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \left(i \left(- \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right)$$
=
// ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ \ // ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ \ / ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ || / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\| | || / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\| | | / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\| | / 2 / / 2 \\ / 2 / / 2 \\| || 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| | || 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| ||(1 - 2*re(y))*im(a) - 2*im(y)*re(a) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*re(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------||*im(a)| ||(1 - 2*re(y))*im(a) - 2*im(y)*re(a) - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*re(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------||*im(a)| |(1 - 2*re(y))*im(a) - 2*im(y)*re(a) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*im(a) |(1 - 2*re(y))*im(a) - 2*im(y)*re(a) - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*im(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------||*re(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------||*re(a) |\ \ 2 / \ 2 / / \ \ 2 / \ 2 // | |\ \ 2 / \ 2 / / \ \ 2 / \ 2 // | \ \ 2 / \ 2 / / \ \ 2 / \ 2 / / \ \ 2 / \ 2 // \ \ 2 / \ 2 // I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 2 2 2 2 | | 2 2 2 2 | 2 2 2 2 2 2 2 2 \ im (a) + re (a) im (a) + re (a) / \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a) im (a) + re (a) im (a) + re (a)
$$i \left(- \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + i \left(- \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
producto
/ // ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ \ / ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ \ / // ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ \ / ________________________________________________________________________ ________________________________________________________________________ \ / ________________________________________________________________________ ________________________________________________________________________ \ \ | || / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\| | | / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\| | | || / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\| | | / 2 / / 2 \\ / 2 / / 2 \\ | | / 2 / / 2 \\ / 2 / / 2 \\| | | || 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| | | || 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| | | 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/| 4 / / 2 \ 2 |atan2\(-2 + re(a))*im(a) + im(a)*re(a), - im (a) + (-2 + re(a))*re(a)/|| | | ||(1 - 2*re(y))*im(a) - 2*im(y)*re(a) - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*re(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------||*im(a)| |(1 - 2*re(y))*im(a) - 2*im(y)*re(a) - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*im(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------||*re(a)| | ||(1 - 2*re(y))*im(a) - 2*im(y)*re(a) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*re(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------||*im(a)| |(1 - 2*re(y))*im(a) - 2*im(y)*re(a) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*sin|----------------------------------------------------------------------| + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *cos|----------------------------------------------------------------------|*im(y)|*im(a) |(1 - 2*re(y))*re(a) + 2*im(a)*im(y) + \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *(1 + re(y))*cos|----------------------------------------------------------------------| - \/ \- im (a) + (-2 + re(a))*re(a)/ + ((-2 + re(a))*im(a) + im(a)*re(a)) *im(y)*sin|----------------------------------------------------------------------||*re(a)| | |\ \ 2 / \ 2 / / \ \ 2 / \ 2 // | \ \ 2 / \ 2 / / \ \ 2 / \ 2 // | | |\ \ 2 / \ 2 / / \ \ 2 / \ 2 // | \ \ 2 / \ 2 / / \ \ 2 / \ 2 // | |I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|I*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | | 2 2 2 2 | 2 2 2 2 | | | 2 2 2 2 | 2 2 2 2 | \ \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a) / \ \ im (a) + re (a) im (a) + re (a) / im (a) + re (a) im (a) + re (a) /
$$\left(i \left(- \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) \left(i \left(- \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right) + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{\left(\left(1 - 2 \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(a\right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \left(\operatorname{re}{\left(y\right)} + 1\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + \sqrt[4]{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{im}{\left(a\right)} + \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},\left(\operatorname{re}{\left(a\right)} - 2\right) \operatorname{re}{\left(a\right)} - \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{im}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)}\right) \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}\right)$$
=
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2*re(a) - 6*im (a)*re(y) - 6*re (a)*re(y) - 3*im (a)*im (y) - 3*im (y)*re (a) - 2*I*im(a) - 2*im (y)*re(a) + 2*re (y)*re(a) + 3*im (a)*re (y) + 3*re (a)*re (y) + 4*im(a)*im(y) + 4*re(a)*re(y) - 6*I*im (a)*im(y) - 6*I*re (a)*im(y) - 4*I*im(a)*re(y) - 2*I*re (y)*im(a) + 2*I*im (y)*im(a) + 4*I*im(y)*re(a) + 4*im(a)*im(y)*re(y) + 4*I*im(y)*re(a)*re(y) + 6*I*im (a)*im(y)*re(y) + 6*I*re (a)*im(y)*re(y)
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2
im (a) + re (a)
$$\frac{3 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{re}{\left(y\right)}\right)^{2} + 6 i \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{re}{\left(y\right)} - 3 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 6 i \left(\operatorname{re}{\left(a\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(a\right)} \left(\operatorname{re}{\left(y\right)}\right)^{2} + 4 i \operatorname{re}{\left(a\right)} \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 4 \operatorname{re}{\left(a\right)} \operatorname{re}{\left(y\right)} - 2 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4 i \operatorname{re}{\left(a\right)} \operatorname{im}{\left(y\right)} + 2 \operatorname{re}{\left(a\right)} + 3 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 2 i \left(\operatorname{re}{\left(y\right)}\right)^{2} \operatorname{im}{\left(a\right)} + 6 i \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} \operatorname{im}{\left(y\right)} - 6 \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 4 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)} - 4 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(a\right)} - 3 \left(\operatorname{im}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 6 i \left(\operatorname{im}{\left(a\right)}\right)^{2} \operatorname{im}{\left(y\right)} + 2 i \operatorname{im}{\left(a\right)} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 4 \operatorname{im}{\left(a\right)} \operatorname{im}{\left(y\right)} - 2 i \operatorname{im}{\left(a\right)}}{\left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}}$$
(2*re(a) - 6*im(a)^2*re(y) - 6*re(a)^2*re(y) - 3*im(a)^2*im(y)^2 - 3*im(y)^2*re(a)^2 - 2*i*im(a) - 2*im(y)^2*re(a) + 2*re(y)^2*re(a) + 3*im(a)^2*re(y)^2 + 3*re(a)^2*re(y)^2 + 4*im(a)*im(y) + 4*re(a)*re(y) - 6*i*im(a)^2*im(y) - 6*i*re(a)^2*im(y) - 4*i*im(a)*re(y) - 2*i*re(y)^2*im(a) + 2*i*im(y)^2*im(a) + 4*i*im(y)*re(a) + 4*im(a)*im(y)*re(y) + 4*i*im(y)*re(a)*re(y) + 6*i*im(a)^2*im(y)*re(y) + 6*i*re(a)^2*im(y)*re(y))/(im(a)^2 + re(a)^2)