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Expresiones semejantes
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- x^2y^2+17-x^2-8xy+2xy=0
x^2y^2+17+x^2-8xy+2xy=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 2 x *y + 17 + x - 8*x*y + 2*x*y = 0
$$2 x y + \left(- 8 x y + \left(x^{2} + \left(x^{2} y^{2} + 17\right)\right)\right) = 0$$
Solución detallada
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = y^{2} + 1$$
$$b = - 6 y$$
$$c = 17$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{6 y + \sqrt{- 32 y^{2} - 68}}{2 y^{2} + 2}$$
$$x_{2} = \frac{6 y - \sqrt{- 32 y^{2} - 68}}{2 y^{2} + 2}$$
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = y^{2} + 1$$
$$b = - 6 y$$
$$c = 17$$
, entonces
D = b^2 - 4 * a * c =
(-6*y)^2 - 4 * (1 + y^2) * (17) = -68 - 32*y^2
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{6 y + \sqrt{- 32 y^{2} - 68}}{2 y^{2} + 2}$$
$$x_{2} = \frac{6 y - \sqrt{- 32 y^{2} - 68}}{2 y^{2} + 2}$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$2 x y + \left(- 8 x y + \left(x^{2} + \left(x^{2} y^{2} + 17\right)\right)\right) = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{x^{2} y^{2} + x^{2} - 6 x y + 17}{y^{2} + 1} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{6 y}{y^{2} + 1}$$
$$q = \frac{c}{a}$$
$$q = \frac{17}{y^{2} + 1}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{6 y}{y^{2} + 1}$$
$$x_{1} x_{2} = \frac{17}{y^{2} + 1}$$
$$2 x y + \left(- 8 x y + \left(x^{2} + \left(x^{2} y^{2} + 17\right)\right)\right) = 0$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$\frac{x^{2} y^{2} + x^{2} - 6 x y + 17}{y^{2} + 1} = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - \frac{6 y}{y^{2} + 1}$$
$$q = \frac{c}{a}$$
$$q = \frac{17}{y^{2} + 1}$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{6 y}{y^{2} + 1}$$
$$x_{1} x_{2} = \frac{17}{y^{2} + 1}$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$x^{2} y^{2} + x^{2} - 6 x y + 17 = 0$$
Коэффициент при x равен
$$y^{2} + 1$$
entonces son posibles los casos para y :
Consideremos todos los casos con detalles:
$$x^{2} y^{2} + x^{2} - 6 x y + 17 = 0$$
Коэффициент при x равен
$$y^{2} + 1$$
entonces son posibles los casos para y :
Consideremos todos los casos con detalles:
Gráfica
Respuesta rápida
[src]
// __________________________________________________ \ / __________________________________________________ \ \ / __________________________________________________ \ / __________________________________________________ \
|| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
|| 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| | | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/||
||3*im(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*re(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*im(y)*re(y)| |3*re(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*im(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*im(y)*re(y)
|\ \ 2 // \ \ 2 // | \ \ 2 // \ \ 2 //
x1 = I*|----------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------
| 2 2 | 2 2
| / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2
\ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y)
$$x_{1} = \frac{2 \left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(\frac{\left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)$$
// __________________________________________________ \ / __________________________________________________ \ \ / __________________________________________________ \ / __________________________________________________ \
|| / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
|| 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| | | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/||
||3*im(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*re(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*im(y)*re(y)| |3*re(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*im(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*im(y)*re(y)
|\ \ 2 // \ \ 2 // | \ \ 2 // \ \ 2 //
x2 = I*|----------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------
| 2 2 | 2 2
| / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2
\ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y)
$$x_{2} = \frac{2 \left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(\frac{\left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)$$
x2 = 2*(((-8*re(y)^2 + 8*im(y)^2 - 17)^2 + 256*re(y)^2*im(y)^2)^(1/4)*sin(atan2(-16*re(y)*im(y, -8*re(y)^2 + 8*im(y)^2 - 17)/2) + 3*im(y))*re(y)*im(y)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) + (((-8*re(y)^2 + 8*im(y)^2 - 17)^2 + 256*re(y)^2*im(y)^2)^(1/4)*cos(atan2(-16*re(y)*im(y), -8*re(y)^2 + 8*im(y)^2 - 17)/2) + 3*re(y))*(re(y)^2 - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) + i*((((-8*re(y)^2 + 8*im(y)^2 - 17)^2 + 256*re(y)^2*im(y)^2)^(1/4)*sin(atan2(-16*re(y)*im(y), -8*re(y)^2 + 8*im(y)^2 - 17)/2) + 3*im(y))*(re(y)^2 - im(y)^2 + 1)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^2) - 2*(((-8*re(y)^2 + 8*im(y)^2 - 17)^2 + 256*re(y)^2*im(y)^2)^(1/4)*cos(atan2(-16*re(y)*im(y), -8*re(y)^2 + 8*im(y)^2 - 17)/2) + 3*re(y))*re(y)*im(y)/((re(y)^2 - im(y)^2 + 1)^2 + 4*re(y)^2*im(y)^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 \\| || 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| | | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| || 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| | | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| ||3*im(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*re(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*im(y)*re(y)| |3*re(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*im(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*im(y)*re(y) ||3*im(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*re(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*im(y)*re(y)| |3*re(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*im(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*im(y)*re(y) |\ \ 2 // \ \ 2 // | \ \ 2 // \ \ 2 // |\ \ 2 // \ \ 2 // | \ \ 2 // \ \ 2 // I*|----------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------- + I*|----------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------- | 2 2 | 2 2 | 2 2 | 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y)
$$\left(\frac{2 \left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(\frac{\left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)\right) + \left(\frac{2 \left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(\frac{\left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)\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 \\| || 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| | || 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| | | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| ||3*im(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*re(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*im(y)*re(y)| ||3*im(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*re(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*im(y)*re(y)| |3*re(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*\1 + re (y) - im (y)/ |3*re(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*im(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*im(y)*re(y) 2*|3*im(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*im(y)*re(y) |\ \ 2 // \ \ 2 // | |\ \ 2 // \ \ 2 // | \ \ 2 // \ \ 2 // \ \ 2 // \ \ 2 // I*|----------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------| + I*|----------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------- | 2 2 | | 2 2 | 2 2 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 | | / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 / 2 2 \ 2 2 \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y)
$$\frac{2 \left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{2 \left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(\frac{\left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right) + i \left(\frac{\left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)$$
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 \\| | | || 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| | | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| | | || 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| | | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| / 2 2 \ | 4 / / 2 2 \ 2 2 |atan2\-16*im(y)*re(y), -17 - 8*re (y) + 8*im (y)/|| | | ||3*im(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*re(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*im(y)*re(y)| |3*re(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*im(y) - \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*im(y)*re(y)| | ||3*im(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*re(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*im(y)*re(y)| |3*re(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *cos|-------------------------------------------------||*\1 + re (y) - im (y)/ 2*|3*im(y) + \/ \-17 - 8*re (y) + 8*im (y)/ + 256*im (y)*re (y) *sin|-------------------------------------------------||*im(y)*re(y)| | |\ \ 2 // \ \ 2 // | \ \ 2 // \ \ 2 // | | |\ \ 2 // \ \ 2 // | \ \ 2 // \ \ 2 // | |I*|----------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------|*|I*|----------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------| | | 2 2 | 2 2 | | | 2 2 | 2 2 | | | / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 | | | / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2 | \ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \ \ \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) / \1 + re (y) - im (y)/ + 4*im (y)*re (y) \1 + re (y) - im (y)/ + 4*im (y)*re (y) /
$$\left(\frac{2 \left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(\frac{\left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(- \sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)\right) \left(\frac{2 \left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + \frac{\left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} + i \left(\frac{\left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{im}{\left(y\right)}\right) \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} - \frac{2 \left(\sqrt[4]{\left(- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17\right)^{2} + 256 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 16 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)},- 8 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 8 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 17 \right)}}{2} \right)} + 3 \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{\left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1\right)^{2} + 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2}}\right)\right)$$
=
2 2
17 - 17*im (y) + 17*re (y) - 34*I*im(y)*re(y)
-----------------------------------------------------------
4 4 2 2 2 2
1 + im (y) + re (y) - 2*im (y) + 2*re (y) + 2*im (y)*re (y)
$$\frac{17 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 34 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 17 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 17}{\left(\operatorname{re}{\left(y\right)}\right)^{4} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} + 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} + \left(\operatorname{im}{\left(y\right)}\right)^{4} - 2 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 1}$$
(17 - 17*im(y)^2 + 17*re(y)^2 - 34*i*im(y)*re(y))/(1 + im(y)^4 + re(y)^4 - 2*im(y)^2 + 2*re(y)^2 + 2*im(y)^2*re(y)^2)