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Expresiones idénticas
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xy=4Scrt(2x^2+y^2+y) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
_______________
/ 2 2
x*y = 4*\/ 2*x + y + y
$$x y = 4 \sqrt{y + \left(2 x^{2} + y^{2}\right)}$$
Solución detallada
Tenemos la ecuación
$$x y = 4 \sqrt{y + \left(2 x^{2} + y^{2}\right)}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- 4 \sqrt{2 x^{2} + y^{2} + y} = - x y$$
Elevemos las dos partes de la ecuación a la potencia 2
$$32 x^{2} + 16 y^{2} + 16 y = x^{2} y^{2}$$
$$32 x^{2} + 16 y^{2} + 16 y = x^{2} y^{2}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- x^{2} y^{2} + 32 x^{2} + 16 y^{2} + 16 y = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 16 - x^{2}$$
$$b = 16$$
$$c = 32 x^{2}$$
, entonces
La ecuación tiene dos raíces.
o
$$y_{1} = \frac{\sqrt{- 32 x^{2} \left(64 - 4 x^{2}\right) + 256} - 16}{32 - 2 x^{2}}$$
$$y_{2} = \frac{- \sqrt{- 32 x^{2} \left(64 - 4 x^{2}\right) + 256} - 16}{32 - 2 x^{2}}$$
$$x y = 4 \sqrt{y + \left(2 x^{2} + y^{2}\right)}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- 4 \sqrt{2 x^{2} + y^{2} + y} = - x y$$
Elevemos las dos partes de la ecuación a la potencia 2
$$32 x^{2} + 16 y^{2} + 16 y = x^{2} y^{2}$$
$$32 x^{2} + 16 y^{2} + 16 y = x^{2} y^{2}$$
Transpongamos la parte derecha de la ecuación miembro izquierdo de la ecuación con el signo negativo
$$- x^{2} y^{2} + 32 x^{2} + 16 y^{2} + 16 y = 0$$
Es la ecuación de la forma
a*y^2 + b*y + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = 16 - x^{2}$$
$$b = 16$$
$$c = 32 x^{2}$$
, entonces
D = b^2 - 4 * a * c =
(16)^2 - 4 * (16 - x^2) * (32*x^2) = 256 - 32*x^2*(64 - 4*x^2)
La ecuación tiene dos raíces.
y1 = (-b + sqrt(D)) / (2*a)
y2 = (-b - sqrt(D)) / (2*a)
o
$$y_{1} = \frac{\sqrt{- 32 x^{2} \left(64 - 4 x^{2}\right) + 256} - 16}{32 - 2 x^{2}}$$
$$y_{2} = \frac{- \sqrt{- 32 x^{2} \left(64 - 4 x^{2}\right) + 256} - 16}{32 - 2 x^{2}}$$
Gráfica
Respuesta rápida
[src]
/ ______________________________________________________________________________________________________________________________ / ______________________________________________________________________________________________________________________________ \ \ / ______________________________________________________________________________________________________________________________ \ ______________________________________________________________________________________________________________________________
| / 2 2 / / 3 3 2 4 4 2 2 2 \\ | / 2 2 / / 3 3 2 4 4 2 2 2 \\| | | / 2 2 / / 3 3 2 4 4 2 2 2 \\| / 2 2 / / 3 3 2 4 4 2 2 2 \\
| 4 / / 3 3 \ / 2 4 4 2 2 2 \ / 2 2 \ |atan2\-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x), 4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/| | 4 / / 3 3 \ / 2 4 4 2 2 2 \ |atan2\-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x), 4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/|| | | 4 / / 3 3 \ / 2 4 4 2 2 2 \ |atan2\-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x), 4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/|| / 2 2 \ 4 / / 3 3 \ / 2 4 4 2 2 2 \ |atan2\-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x), 4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/|
| 4*\/ \-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x)/ + \4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/ *\-16 + re (x) - im (x)/*sin|----------------------------------------------------------------------------------------------------------------------------| 2*|8 - 4*\/ \-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x)/ + \4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/ *cos|----------------------------------------------------------------------------------------------------------------------------||*im(x)*re(x)| |8 - 4*\/ \-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x)/ + \4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/ *cos|----------------------------------------------------------------------------------------------------------------------------||*\-16 + re (x) - im (x)/ 8*\/ \-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x)/ + \4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/ *im(x)*re(x)*sin|----------------------------------------------------------------------------------------------------------------------------|
| \ 2 / \ \ 2 // | \ \ 2 // \ 2 /
y1 = I*|- ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 2 | 2 2
| / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2
\ \-16 + re (x) - im (x)/ + 4*im (x)*re (x) \-16 + re (x) - im (x)/ + 4*im (x)*re (x) / \-16 + re (x) - im (x)/ + 4*im (x)*re (x) \-16 + re (x) - im (x)/ + 4*im (x)*re (x)
$$y_{1} = \frac{\left(- 4 \sqrt[4]{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}\right)^{2} + \left(2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4 \right)}}{2} \right)} + 8\right) \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 16\right)}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 16\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} + i \left(- \frac{2 \left(- 4 \sqrt[4]{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}\right)^{2} + \left(2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4 \right)}}{2} \right)} + 8\right) \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 16\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} - \frac{4 \sqrt[4]{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}\right)^{2} + \left(2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4\right)^{2}} \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 16\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4 \right)}}{2} \right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 16\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) - \frac{8 \sqrt[4]{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}\right)^{2} + \left(2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4 \right)}}{2} \right)} \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 16\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
/ / ______________________________________________________________________________________________________________________________ \ ______________________________________________________________________________________________________________________________ \ / ______________________________________________________________________________________________________________________________ \ ______________________________________________________________________________________________________________________________
| | / 2 2 / / 3 3 2 4 4 2 2 2 \\| / 2 2 / / 3 3 2 4 4 2 2 2 \\| | / 2 2 / / 3 3 2 4 4 2 2 2 \\| / 2 2 / / 3 3 2 4 4 2 2 2 \\
| | 4 / / 3 3 \ / 2 4 4 2 2 2 \ |atan2\-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x), 4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/|| 4 / / 3 3 \ / 2 4 4 2 2 2 \ / 2 2 \ |atan2\-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x), 4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/|| | 4 / / 3 3 \ / 2 4 4 2 2 2 \ |atan2\-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x), 4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/|| / 2 2 \ 4 / / 3 3 \ / 2 4 4 2 2 2 \ |atan2\-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x), 4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/|
| 2*|8 + 4*\/ \-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x)/ + \4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/ *cos|----------------------------------------------------------------------------------------------------------------------------||*im(x)*re(x) 4*\/ \-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x)/ + \4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/ *\-16 + re (x) - im (x)/*sin|----------------------------------------------------------------------------------------------------------------------------|| |8 + 4*\/ \-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x)/ + \4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/ *cos|----------------------------------------------------------------------------------------------------------------------------||*\-16 + re (x) - im (x)/ 8*\/ \-64*im(x)*re(x) - 8*im (x)*re(x) + 8*re (x)*im(x)/ + \4 - 32*re (x) + 2*im (x) + 2*re (x) + 32*im (x) - 12*im (x)*re (x)/ *im(x)*re(x)*sin|----------------------------------------------------------------------------------------------------------------------------|
| \ \ 2 // \ 2 /| \ \ 2 // \ 2 /
y2 = I*|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| 2 2 | 2 2
| / 2 2 \ 2 2 / 2 2 \ 2 2 | / 2 2 \ 2 2 / 2 2 \ 2 2
\ \-16 + re (x) - im (x)/ + 4*im (x)*re (x) \-16 + re (x) - im (x)/ + 4*im (x)*re (x) / \-16 + re (x) - im (x)/ + 4*im (x)*re (x) \-16 + re (x) - im (x)/ + 4*im (x)*re (x)
$$y_{2} = \frac{\left(4 \sqrt[4]{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}\right)^{2} + \left(2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4 \right)}}{2} \right)} + 8\right) \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 16\right)}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 16\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} + i \left(- \frac{2 \left(4 \sqrt[4]{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}\right)^{2} + \left(2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4 \right)}}{2} \right)} + 8\right) \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 16\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}} + \frac{4 \sqrt[4]{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}\right)^{2} + \left(2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4\right)^{2}} \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 16\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4 \right)}}{2} \right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 16\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right) + \frac{8 \sqrt[4]{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}\right)^{2} + \left(2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \left(\operatorname{re}{\left(x\right)}\right)^{3} \operatorname{im}{\left(x\right)} - 8 \operatorname{re}{\left(x\right)} \left(\operatorname{im}{\left(x\right)}\right)^{3} - 64 \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)},2 \left(\operatorname{re}{\left(x\right)}\right)^{4} - 12 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2} - 32 \left(\operatorname{re}{\left(x\right)}\right)^{2} + 2 \left(\operatorname{im}{\left(x\right)}\right)^{4} + 32 \left(\operatorname{im}{\left(x\right)}\right)^{2} + 4 \right)}}{2} \right)} \operatorname{re}{\left(x\right)} \operatorname{im}{\left(x\right)}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} - \left(\operatorname{im}{\left(x\right)}\right)^{2} - 16\right)^{2} + 4 \left(\operatorname{re}{\left(x\right)}\right)^{2} \left(\operatorname{im}{\left(x\right)}\right)^{2}}$$
y2 = (4*((8*re(x)^3*im(x) - 8*re(x)*im(x)^3 - 64*re(x)*im(x))^2 + (2*re(x)^4 - 12*re(x)^2*im(x)^2 - 32*re(x)^2 + 2*im(x)^4 + 32*im(x)^2 + 4)^2)^(1/4)*cos(atan2(8*re(x)^3*im(x) - 8*re(x)*im(x)^3 - 64*re(x)*im(x, 2*re(x)^4 - 12*re(x)^2*im(x)^2 - 32*re(x)^2 + 2*im(x)^4 + 32*im(x)^2 + 4)/2) + 8)*(re(x)^2 - im(x)^2 - 16)/((re(x)^2 - im(x)^2 - 16)^2 + 4*re(x)^2*im(x)^2) + i*(-2*(4*((8*re(x)^3*im(x) - 8*re(x)*im(x)^3 - 64*re(x)*im(x))^2 + (2*re(x)^4 - 12*re(x)^2*im(x)^2 - 32*re(x)^2 + 2*im(x)^4 + 32*im(x)^2 + 4)^2)^(1/4)*cos(atan2(8*re(x)^3*im(x) - 8*re(x)*im(x)^3 - 64*re(x)*im(x), 2*re(x)^4 - 12*re(x)^2*im(x)^2 - 32*re(x)^2 + 2*im(x)^4 + 32*im(x)^2 + 4)/2) + 8)*re(x)*im(x)/((re(x)^2 - im(x)^2 - 16)^2 + 4*re(x)^2*im(x)^2) + 4*((8*re(x)^3*im(x) - 8*re(x)*im(x)^3 - 64*re(x)*im(x))^2 + (2*re(x)^4 - 12*re(x)^2*im(x)^2 - 32*re(x)^2 + 2*im(x)^4 + 32*im(x)^2 + 4)^2)^(1/4)*(re(x)^2 - im(x)^2 - 16)*sin(atan2(8*re(x)^3*im(x) - 8*re(x)*im(x)^3 - 64*re(x)*im(x), 2*re(x)^4 - 12*re(x)^2*im(x)^2 - 32*re(x)^2 + 2*im(x)^4 + 32*im(x)^2 + 4)/2)/((re(x)^2 - im(x)^2 - 16)^2 + 4*re(x)^2*im(x)^2)) + 8*((8*re(x)^3*im(x) - 8*re(x)*im(x)^3 - 64*re(x)*im(x))^2 + (2*re(x)^4 - 12*re(x)^2*im(x)^2 - 32*re(x)^2 + 2*im(x)^4 + 32*im(x)^2 + 4)^2)^(1/4)*sin(atan2(8*re(x)^3*im(x) - 8*re(x)*im(x)^3 - 64*re(x)*im(x), 2*re(x)^4 - 12*re(x)^2*im(x)^2 - 32*re(x)^2 + 2*im(x)^4 + 32*im(x)^2 + 4)/2)*re(x)*im(x)/((re(x)^2 - im(x)^2 - 16)^2 + 4*re(x)^2*im(x)^2))