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Expresiones semejantes
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- -0,5*i(x-i*y)+i(0,5*x^2+i*x*y)=-0,5-i
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- -0,5*i(x-i*y)+i(0,5*x^2+i*x*y)=+0,5+i
- -0,5*i(x-i*y)+i(0,5*x^2-i*x*y)=-0,5+i
-0,5*i(x-i*y)+i(0,5*x^2+i*x*y)=-0,5+i la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
/ 2 \ -I |x | ---*(x - I*y) + I*|-- + I*x*y| = -1/2 + I 2 \2 /
$$- \frac{i}{2} \left(x - i y\right) + i \left(\frac{x^{2}}{2} + y i x\right) = - \frac{1}{2} + i$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$- \frac{i}{2} \left(x - i y\right) + i \left(\frac{x^{2}}{2} + y i x\right) = - \frac{1}{2} + i$$
en
$$\left(- \frac{i}{2} \left(x - i y\right) + i \left(\frac{x^{2}}{2} + y i x\right)\right) + \left(\frac{1}{2} - i\right) = 0$$
Abramos la expresión en la ecuación
$$\left(- \frac{i}{2} \left(x - i y\right) + i \left(\frac{x^{2}}{2} + y i x\right)\right) + \left(\frac{1}{2} - i\right) = 0$$
Obtenemos la ecuación cuadrática
$$\frac{i x^{2}}{2} - x y - \frac{i x}{2} - \frac{y}{2} + \frac{1}{2} - i = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = \frac{i}{2}$$
$$b = - y - \frac{i}{2}$$
$$c = - \frac{y}{2} + \frac{1}{2} - i$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = - i \left(y + \sqrt{\left(- y - \frac{i}{2}\right)^{2} - 2 i \left(- \frac{y}{2} + \frac{1}{2} - i\right)} + \frac{i}{2}\right)$$
$$x_{2} = - i \left(y - \sqrt{\left(- y - \frac{i}{2}\right)^{2} - 2 i \left(- \frac{y}{2} + \frac{1}{2} - i\right)} + \frac{i}{2}\right)$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$- \frac{i}{2} \left(x - i y\right) + i \left(\frac{x^{2}}{2} + y i x\right) = - \frac{1}{2} + i$$
en
$$\left(- \frac{i}{2} \left(x - i y\right) + i \left(\frac{x^{2}}{2} + y i x\right)\right) + \left(\frac{1}{2} - i\right) = 0$$
Abramos la expresión en la ecuación
$$\left(- \frac{i}{2} \left(x - i y\right) + i \left(\frac{x^{2}}{2} + y i x\right)\right) + \left(\frac{1}{2} - i\right) = 0$$
Obtenemos la ecuación cuadrática
$$\frac{i x^{2}}{2} - x y - \frac{i x}{2} - \frac{y}{2} + \frac{1}{2} - i = 0$$
Es la ecuación de la forma
a*x^2 + b*x + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = \frac{i}{2}$$
$$b = - y - \frac{i}{2}$$
$$c = - \frac{y}{2} + \frac{1}{2} - i$$
, entonces
D = b^2 - 4 * a * c =
(-y - i/2)^2 - 4 * (i/2) * (1/2 - i - y/2) = (-y - i/2)^2 - 2*i*(1/2 - i - y/2)
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = - i \left(y + \sqrt{\left(- y - \frac{i}{2}\right)^{2} - 2 i \left(- \frac{y}{2} + \frac{1}{2} - i\right)} + \frac{i}{2}\right)$$
$$x_{2} = - i \left(y - \sqrt{\left(- y - \frac{i}{2}\right)^{2} - 2 i \left(- \frac{y}{2} + \frac{1}{2} - i\right)} + \frac{i}{2}\right)$$
Gráfica
Respuesta rápida
[src]
/ _________________________________________________________________________ \ _________________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/|| 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/|
| \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *cos|-----------------------------------------------------------------------|| \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *sin|-----------------------------------------------------------------------|
1 | \ 2 /| \ 2 /
x1 = - + I*|-re(y) + ----------------------------------------------------------------------------------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------------------------------- + im(y)
2 \ 2 / 2
$$x_{1} = i \left(\frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} - \operatorname{re}{\left(y\right)}\right) - \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)} + \frac{1}{2}$$
/ _________________________________________________________________________ \ _________________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/|| 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/|
| \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *cos|-----------------------------------------------------------------------|| \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *sin|-----------------------------------------------------------------------|
1 | \ 2 /| \ 2 /
x2 = - + I*|-re(y) - ----------------------------------------------------------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------- + im(y)
2 \ 2 / 2
$$x_{2} = i \left(- \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} - \operatorname{re}{\left(y\right)}\right) + \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)} + \frac{1}{2}$$
x2 = i*(-((8*re(y)*im(y) + 8*re(y) - 4)^2 + (4*re(y)^2 - 4*im(y)^2 - 8*im(y) - 9)^2)^(1/4)*cos(atan2(8*re(y)*im(y) + 8*re(y - 4, 4*re(y)^2 - 4*im(y)^2 - 8*im(y) - 9)/2)/2 - re(y)) + ((8*re(y)*im(y) + 8*re(y) - 4)^2 + (4*re(y)^2 - 4*im(y)^2 - 8*im(y) - 9)^2)^(1/4)*sin(atan2(8*re(y)*im(y) + 8*re(y) - 4, 4*re(y)^2 - 4*im(y)^2 - 8*im(y) - 9)/2)/2 + im(y) + 1/2)
Suma y producto de raíces
[src]
suma
/ _________________________________________________________________________ \ _________________________________________________________________________ / _________________________________________________________________________ \ _________________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\ | / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/|| 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/| | 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/|| 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/|
| \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *cos|-----------------------------------------------------------------------|| \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *sin|-----------------------------------------------------------------------| | \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *cos|-----------------------------------------------------------------------|| \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *sin|-----------------------------------------------------------------------|
1 | \ 2 /| \ 2 / 1 | \ 2 /| \ 2 /
- + I*|-re(y) + ----------------------------------------------------------------------------------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------------------------------- + im(y) + - + I*|-re(y) - ----------------------------------------------------------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------- + im(y)
2 \ 2 / 2 2 \ 2 / 2
$$\left(i \left(- \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} - \operatorname{re}{\left(y\right)}\right) + \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)} + \frac{1}{2}\right) + \left(i \left(\frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} - \operatorname{re}{\left(y\right)}\right) - \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)} + \frac{1}{2}\right)$$
=
/ _________________________________________________________________________ \ / _________________________________________________________________________ \
| / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
| 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/|| | 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/||
| \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *cos|-----------------------------------------------------------------------|| | \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *cos|-----------------------------------------------------------------------||
| \ 2 /| | \ 2 /|
1 + 2*im(y) + I*|-re(y) + ----------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|-re(y) - ----------------------------------------------------------------------------------------------------------------------------------------------------------|
\ 2 / \ 2 /
$$i \left(- \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} - \operatorname{re}{\left(y\right)}\right) + i \left(\frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} - \operatorname{re}{\left(y\right)}\right) + 2 \operatorname{im}{\left(y\right)} + 1$$
producto
/ / _________________________________________________________________________ \ _________________________________________________________________________ \ / / _________________________________________________________________________ \ _________________________________________________________________________ \ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\| / 2 / / 2 2 \\ | | | 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/|| 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/| | | | 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/|| 4 / 2 / 2 2 \ |atan2\-4 + 8*re(y) + 8*im(y)*re(y), -9 - 8*im(y) - 4*im (y) + 4*re (y)/| | | | \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *cos|-----------------------------------------------------------------------|| \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *sin|-----------------------------------------------------------------------| | | | \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *cos|-----------------------------------------------------------------------|| \/ (-4 + 8*re(y) + 8*im(y)*re(y)) + \-9 - 8*im(y) - 4*im (y) + 4*re (y)/ *sin|-----------------------------------------------------------------------| | |1 | \ 2 /| \ 2 / | |1 | \ 2 /| \ 2 / | |- + I*|-re(y) + ----------------------------------------------------------------------------------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------------------------------- + im(y)|*|- + I*|-re(y) - ----------------------------------------------------------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------- + im(y)| \2 \ 2 / 2 / \2 \ 2 / 2 /
$$\left(i \left(- \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} - \operatorname{re}{\left(y\right)}\right) + \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)} + \frac{1}{2}\right) \left(i \left(\frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} - \operatorname{re}{\left(y\right)}\right) - \frac{\sqrt[4]{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4\right)^{2} + \left(4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 8 \operatorname{re}{\left(y\right)} - 4,4 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 8 \operatorname{im}{\left(y\right)} - 9 \right)}}{2} \right)}}{2} + \operatorname{im}{\left(y\right)} + \frac{1}{2}\right)$$
=
-2 - I - im(y) + I*re(y)
$$i \operatorname{re}{\left(y\right)} - \operatorname{im}{\left(y\right)} - 2 - i$$
-2 - i - im(y) + i*re(y)