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- La ecuación:
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Ecuación x=(x+1)/2
- Ecuación (x-6)(-5x-9)=0
-
Ecuación x^2-14*x+33=0
-
Ecuación x^2+6=5x
- Expresar {x} en función de y en la ecuación:
- -13*x-19*y=17
- -9*x-12*y=-19
- -17*x-12*y=-9
- -8*x+3*y=-4
- Derivada de:
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-4
- Integral de d{x}:
- -4
- Límite de la función:
- -4
-
Expresiones idénticas
- (y-3x)^ dos +(x+y- dos)^ dos =- cuatro
- (y menos 3x) al cuadrado más (x más y menos 2) al cuadrado es igual a menos 4
- (y menos 3x) en el grado dos más (x más y menos dos) en el grado dos es igual a menos cuatro
- (y-3x)2+(x+y-2)2=-4
- y-3x2+x+y-22=-4
- (y-3x)²+(x+y-2)²=-4
- (y-3x) en el grado 2+(x+y-2) en el grado 2=-4
- y-3x^2+x+y-2^2=-4
-
Expresiones semejantes
- (y+3x)^2+(x+y-2)^2=-4
- (y-3x)^2+(x+y-2)^2=+4
- (y-3x)^2+(x-y-2)^2=-4
- (y-3x)^2+(x+y+2)^2=-4
- (y-3x)^2-(x+y-2)^2=-4
(y-3x)^2+(x+y-2)^2=-4 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 (y - 3*x) + (x + y - 2) = -4
$$\left(- 3 x + y\right)^{2} + \left(\left(x + y\right) - 2\right)^{2} = -4$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$\left(- 3 x + y\right)^{2} + \left(\left(x + y\right) - 2\right)^{2} = -4$$
en
$$\left(\left(- 3 x + y\right)^{2} + \left(\left(x + y\right) - 2\right)^{2}\right) + 4 = 0$$
Abramos la expresión en la ecuación
$$\left(\left(- 3 x + y\right)^{2} + \left(\left(x + y\right) - 2\right)^{2}\right) + 4 = 0$$
Obtenemos la ecuación cuadrática
$$10 x^{2} - 4 x y - 4 x + 2 y^{2} - 4 y + 8 = 0$$
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
$$a = 10$$
$$b = - 4 y - 4$$
$$c = 2 y^{2} - 4 y + 8$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = \frac{y}{5} + \frac{\sqrt{- 80 y^{2} + 160 y + \left(- 4 y - 4\right)^{2} - 320}}{20} + \frac{1}{5}$$
$$x_{2} = \frac{y}{5} - \frac{\sqrt{- 80 y^{2} + 160 y + \left(- 4 y - 4\right)^{2} - 320}}{20} + \frac{1}{5}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$\left(- 3 x + y\right)^{2} + \left(\left(x + y\right) - 2\right)^{2} = -4$$
en
$$\left(\left(- 3 x + y\right)^{2} + \left(\left(x + y\right) - 2\right)^{2}\right) + 4 = 0$$
Abramos la expresión en la ecuación
$$\left(\left(- 3 x + y\right)^{2} + \left(\left(x + y\right) - 2\right)^{2}\right) + 4 = 0$$
Obtenemos la ecuación cuadrática
$$10 x^{2} - 4 x y - 4 x + 2 y^{2} - 4 y + 8 = 0$$
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
$$a = 10$$
$$b = - 4 y - 4$$
$$c = 2 y^{2} - 4 y + 8$$
, entonces
D = b^2 - 4 * a * c =
(-4 - 4*y)^2 - 4 * (10) * (8 - 4*y + 2*y^2) = -320 + (-4 - 4*y)^2 - 80*y^2 + 160*y
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = \frac{y}{5} + \frac{\sqrt{- 80 y^{2} + 160 y + \left(- 4 y - 4\right)^{2} - 320}}{20} + \frac{1}{5}$$
$$x_{2} = \frac{y}{5} - \frac{\sqrt{- 80 y^{2} + 160 y + \left(- 4 y - 4\right)^{2} - 320}}{20} + \frac{1}{5}$$
Gráfica
Respuesta rápida
[src]
/ _______________________________________________________________________ \ _______________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/|| 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/|
| \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *sin|---------------------------------------------------------------------|| \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *cos|---------------------------------------------------------------------|
1 re(y) |im(y) \ 2 /| \ 2 /
x1 = - + ----- + I*|----- - ------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------
5 5 \ 5 5 / 5
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{im}{\left(y\right)}}{5}\right) - \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{re}{\left(y\right)}}{5} + \frac{1}{5}$$
/ _______________________________________________________________________ \ _______________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/|| 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/|
| \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *sin|---------------------------------------------------------------------|| \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *cos|---------------------------------------------------------------------|
1 re(y) |im(y) \ 2 /| \ 2 /
x2 = - + ----- + I*|----- + ------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------
5 5 \ 5 5 / 5
$$x_{2} = i \left(\frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{im}{\left(y\right)}}{5}\right) + \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{re}{\left(y\right)}}{5} + \frac{1}{5}$$
x2 = i*(((-8*re(y)*im(y) + 12*im(y))^2 + (-4*re(y)^2 + 12*re(y) + 4*im(y)^2 - 19)^2)^(1/4)*sin(atan2(-8*re(y)*im(y) + 12*im(y, -4*re(y)^2 + 12*re(y) + 4*im(y)^2 - 19)/2)/5 + im(y)/5) + ((-8*re(y)*im(y) + 12*im(y))^2 + (-4*re(y)^2 + 12*re(y) + 4*im(y)^2 - 19)^2)^(1/4)*cos(atan2(-8*re(y)*im(y) + 12*im(y), -4*re(y)^2 + 12*re(y) + 4*im(y)^2 - 19)/2)/5 + re(y)/5 + 1/5)
Suma y producto de raíces
[src]
suma
/ _______________________________________________________________________ \ _______________________________________________________________________ / _______________________________________________________________________ \ _______________________________________________________________________
| / 2 / / 2 2 \\| / 2 / / 2 2 \\ | / 2 / / 2 2 \\| / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/|| 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/| | 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/|| 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/|
| \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *sin|---------------------------------------------------------------------|| \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *cos|---------------------------------------------------------------------| | \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *sin|---------------------------------------------------------------------|| \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *cos|---------------------------------------------------------------------|
1 re(y) |im(y) \ 2 /| \ 2 / 1 re(y) |im(y) \ 2 /| \ 2 /
- + ----- + I*|----- - ------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------ + - + ----- + I*|----- + ------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------
5 5 \ 5 5 / 5 5 5 \ 5 5 / 5
$$\left(i \left(- \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{im}{\left(y\right)}}{5}\right) - \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{re}{\left(y\right)}}{5} + \frac{1}{5}\right) + \left(i \left(\frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{im}{\left(y\right)}}{5}\right) + \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{re}{\left(y\right)}}{5} + \frac{1}{5}\right)$$
=
/ _______________________________________________________________________ \ / _______________________________________________________________________ \
| / 2 / / 2 2 \\| | / 2 / / 2 2 \\|
| 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/|| | 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/||
| \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *sin|---------------------------------------------------------------------|| | \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *sin|---------------------------------------------------------------------||
2 2*re(y) |im(y) \ 2 /| |im(y) \ 2 /|
- + ------- + I*|----- - ------------------------------------------------------------------------------------------------------------------------------------------------------| + I*|----- + ------------------------------------------------------------------------------------------------------------------------------------------------------|
5 5 \ 5 5 / \ 5 5 /
$$i \left(- \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{im}{\left(y\right)}}{5}\right) + i \left(\frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{im}{\left(y\right)}}{5}\right) + \frac{2 \operatorname{re}{\left(y\right)}}{5} + \frac{2}{5}$$
producto
/ / _______________________________________________________________________ \ _______________________________________________________________________ \ / / _______________________________________________________________________ \ _______________________________________________________________________ \ | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | / 2 / / 2 2 \\| / 2 / / 2 2 \\| | | 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/|| 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/|| | | 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/|| 4 / 2 / 2 2 \ |atan2\12*im(y) - 8*im(y)*re(y), -19 - 4*re (y) + 4*im (y) + 12*re(y)/|| | | \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *sin|---------------------------------------------------------------------|| \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *cos|---------------------------------------------------------------------|| | | \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *sin|---------------------------------------------------------------------|| \/ (12*im(y) - 8*im(y)*re(y)) + \-19 - 4*re (y) + 4*im (y) + 12*re(y)/ *cos|---------------------------------------------------------------------|| |1 re(y) |im(y) \ 2 /| \ 2 /| |1 re(y) |im(y) \ 2 /| \ 2 /| |- + ----- + I*|----- - ------------------------------------------------------------------------------------------------------------------------------------------------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------|*|- + ----- + I*|----- + ------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------| \5 5 \ 5 5 / 5 / \5 5 \ 5 5 / 5 /
$$\left(i \left(- \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{im}{\left(y\right)}}{5}\right) - \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{re}{\left(y\right)}}{5} + \frac{1}{5}\right) \left(i \left(\frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{im}{\left(y\right)}}{5}\right) + \frac{\sqrt[4]{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)}\right)^{2} + \left(- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 8 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 12 \operatorname{im}{\left(y\right)},- 4 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 12 \operatorname{re}{\left(y\right)} + 4 \left(\operatorname{im}{\left(y\right)}\right)^{2} - 19 \right)}}{2} \right)}}{5} + \frac{\operatorname{re}{\left(y\right)}}{5} + \frac{1}{5}\right)$$
=
2 2 4 2*re(y) im (y) re (y) 2*I*im(y) 2*I*im(y)*re(y) - - ------- - ------ + ------ - --------- + --------------- 5 5 5 5 5 5
$$\frac{\left(\operatorname{re}{\left(y\right)}\right)^{2}}{5} + \frac{2 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)}}{5} - \frac{2 \operatorname{re}{\left(y\right)}}{5} - \frac{\left(\operatorname{im}{\left(y\right)}\right)^{2}}{5} - \frac{2 i \operatorname{im}{\left(y\right)}}{5} + \frac{4}{5}$$
4/5 - 2*re(y)/5 - im(y)^2/5 + re(y)^2/5 - 2*i*im(y)/5 + 2*i*im(y)*re(y)/5