Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación |x^2-1|-|x-3|=7
-
Ecuación 2*x^2+6*x+9=0
-
Ecuación 2^2-x-1=x^2-5*x-(-1-x^2)
-
Ecuación 2x=18-x
- Expresar {x} en función de y en la ecuación:
- 15*x+15*y=16
- 4*x-7*y=12
- -5*x+6*y=19
- 1*x-17*y=-12
-
Expresiones idénticas
- z=x^ dos + dos *y^ dos - dos *x*y- diez *x+ diez *y+ veinte
- z es igual a x al cuadrado más 2 multiplicar por y al cuadrado menos 2 multiplicar por x multiplicar por y menos 10 multiplicar por x más 10 multiplicar por y más 20
- z es igual a x en el grado dos más dos multiplicar por y en el grado dos menos dos multiplicar por x multiplicar por y menos diez multiplicar por x más diez multiplicar por y más veinte
- z=x2+2*y2-2*x*y-10*x+10*y+20
- z=x²+2*y²-2*x*y-10*x+10*y+20
- z=x en el grado 2+2*y en el grado 2-2*x*y-10*x+10*y+20
- z=x^2+2y^2-2xy-10x+10y+20
- z=x2+2y2-2xy-10x+10y+20
-
Expresiones semejantes
- z=x^2+2*y^2-2*x*y-10*x+10*y-20
- z=x^2+2*y^2+2*x*y-10*x+10*y+20
- z=x^2+2*y^2-2*x*y-10*x-10*y+20
- z=x^2+2*y^2-2*x*y+10*x+10*y+20
- z=x^2-2*y^2-2*x*y-10*x+10*y+20
z=x^2+2*y^2-2*x*y-10*x+10*y+20 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 2 z = x + 2*y - 2*x*y - 10*x + 10*y + 20
$$z = \left(10 y + \left(- 10 x + \left(- 2 x y + \left(x^{2} + 2 y^{2}\right)\right)\right)\right) + 20$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$z = \left(10 y + \left(- 10 x + \left(- 2 x y + \left(x^{2} + 2 y^{2}\right)\right)\right)\right) + 20$$
en
$$z + \left(\left(- 10 y + \left(10 x + \left(2 x y + \left(- x^{2} - 2 y^{2}\right)\right)\right)\right) - 20\right) = 0$$
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
$$a = -1$$
$$b = 2 y + 10$$
$$c = - 2 y^{2} - 10 y + z - 20$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = y - \frac{\sqrt{- 8 y^{2} - 40 y + 4 z + \left(2 y + 10\right)^{2} - 80}}{2} + 5$$
$$x_{2} = y + \frac{\sqrt{- 8 y^{2} - 40 y + 4 z + \left(2 y + 10\right)^{2} - 80}}{2} + 5$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$z = \left(10 y + \left(- 10 x + \left(- 2 x y + \left(x^{2} + 2 y^{2}\right)\right)\right)\right) + 20$$
en
$$z + \left(\left(- 10 y + \left(10 x + \left(2 x y + \left(- x^{2} - 2 y^{2}\right)\right)\right)\right) - 20\right) = 0$$
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
$$a = -1$$
$$b = 2 y + 10$$
$$c = - 2 y^{2} - 10 y + z - 20$$
, entonces
D = b^2 - 4 * a * c =
(10 + 2*y)^2 - 4 * (-1) * (-20 + z - 10*y - 2*y^2) = -80 + (10 + 2*y)^2 - 40*y - 8*y^2 + 4*z
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = y - \frac{\sqrt{- 8 y^{2} - 40 y + 4 z + \left(2 y + 10\right)^{2} - 80}}{2} + 5$$
$$x_{2} = y + \frac{\sqrt{- 8 y^{2} - 40 y + 4 z + \left(2 y + 10\right)^{2} - 80}}{2} + 5$$
Teorema de Cardano-Vieta
reescribamos la ecuación
$$z = \left(10 y + \left(- 10 x + \left(- 2 x y + \left(x^{2} + 2 y^{2}\right)\right)\right)\right) + 20$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 2 x y - 10 x + 2 y^{2} + 10 y - z + 20 = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - 2 y - 10$$
$$q = \frac{c}{a}$$
$$q = 2 y^{2} + 10 y - z + 20$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2 y + 10$$
$$x_{1} x_{2} = 2 y^{2} + 10 y - z + 20$$
$$z = \left(10 y + \left(- 10 x + \left(- 2 x y + \left(x^{2} + 2 y^{2}\right)\right)\right)\right) + 20$$
de
$$a x^{2} + b x + c = 0$$
como ecuación cuadrática reducida
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 2 x y - 10 x + 2 y^{2} + 10 y - z + 20 = 0$$
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = - 2 y - 10$$
$$q = \frac{c}{a}$$
$$q = 2 y^{2} + 10 y - z + 20$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2 y + 10$$
$$x_{1} x_{2} = 2 y^{2} + 10 y - z + 20$$
Gráfica
Respuesta rápida
[src]
/ ____________________________________________________________ \ ____________________________________________________________
| / 2 / / 2 2 \\ | / 2 / / 2 2 \\
| 4 / 2 / 2 2 \ |atan2\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/| | 4 / 2 / 2 2 \ |atan2\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/|
x1 = 5 + I*|- \/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *sin|----------------------------------------------------------| + im(y)| - \/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *cos|----------------------------------------------------------| + re(y)
\ \ 2 / / \ 2 /
$$x_{1} = i \left(- \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{im}{\left(y\right)}\right) - \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{re}{\left(y\right)} + 5$$
/ ____________________________________________________________ \ ____________________________________________________________
| / 2 / / 2 2 \\ | / 2 / / 2 2 \\
|4 / 2 / 2 2 \ |atan2\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/| | 4 / 2 / 2 2 \ |atan2\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/|
x2 = 5 + I*|\/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *sin|----------------------------------------------------------| + im(y)| + \/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *cos|----------------------------------------------------------| + re(y)
\ \ 2 / / \ 2 /
$$x_{2} = i \left(\sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{im}{\left(y\right)}\right) + \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{re}{\left(y\right)} + 5$$
x2 = i*(((-2*re(y)*im(y) + im(z))^2 + (-re(y)^2 + re(z) + im(y)^2 + 5)^2)^(1/4)*sin(atan2(-2*re(y)*im(y) + im(z, -re(y)^2 + re(z) + im(y)^2 + 5)/2) + im(y)) + ((-2*re(y)*im(y) + im(z))^2 + (-re(y)^2 + re(z) + im(y)^2 + 5)^2)^(1/4)*cos(atan2(-2*re(y)*im(y) + im(z), -re(y)^2 + re(z) + im(y)^2 + 5)/2) + re(y) + 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\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/| | 4 / 2 / 2 2 \ |atan2\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/| |4 / 2 / 2 2 \ |atan2\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/| | 4 / 2 / 2 2 \ |atan2\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/|
5 + I*|- \/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *sin|----------------------------------------------------------| + im(y)| - \/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *cos|----------------------------------------------------------| + re(y) + 5 + I*|\/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *sin|----------------------------------------------------------| + im(y)| + \/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *cos|----------------------------------------------------------| + re(y)
\ \ 2 / / \ 2 / \ \ 2 / / \ 2 /
$$\left(i \left(- \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{im}{\left(y\right)}\right) - \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{re}{\left(y\right)} + 5\right) + \left(i \left(\sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{im}{\left(y\right)}\right) + \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{re}{\left(y\right)} + 5\right)$$
=
/ ____________________________________________________________ \ / ____________________________________________________________ \
| / 2 / / 2 2 \\ | | / 2 / / 2 2 \\ |
|4 / 2 / 2 2 \ |atan2\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/| | | 4 / 2 / 2 2 \ |atan2\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/| |
10 + 2*re(y) + I*|\/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *sin|----------------------------------------------------------| + im(y)| + I*|- \/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *sin|----------------------------------------------------------| + im(y)|
\ \ 2 / / \ \ 2 / /
$$i \left(- \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{im}{\left(y\right)}\right) + i \left(\sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{im}{\left(y\right)}\right) + 2 \operatorname{re}{\left(y\right)} + 10$$
producto
/ / ____________________________________________________________ \ ____________________________________________________________ \ / / ____________________________________________________________ \ ____________________________________________________________ \ | | / 2 / / 2 2 \\ | / 2 / / 2 2 \\ | | | / 2 / / 2 2 \\ | / 2 / / 2 2 \\ | | | 4 / 2 / 2 2 \ |atan2\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/| | 4 / 2 / 2 2 \ |atan2\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/| | | |4 / 2 / 2 2 \ |atan2\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/| | 4 / 2 / 2 2 \ |atan2\-2*im(y)*re(y) + im(z), 5 + im (y) - re (y) + re(z)/| | |5 + I*|- \/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *sin|----------------------------------------------------------| + im(y)| - \/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *cos|----------------------------------------------------------| + re(y)|*|5 + I*|\/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *sin|----------------------------------------------------------| + im(y)| + \/ (-2*im(y)*re(y) + im(z)) + \5 + im (y) - re (y) + re(z)/ *cos|----------------------------------------------------------| + re(y)| \ \ \ 2 / / \ 2 / / \ \ \ 2 / / \ 2 / /
$$\left(i \left(- \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{im}{\left(y\right)}\right) - \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{re}{\left(y\right)} + 5\right) \left(i \left(\sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{im}{\left(y\right)}\right) + \sqrt[4]{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)}\right)^{2} + \left(- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{im}{\left(z\right)},- \left(\operatorname{re}{\left(y\right)}\right)^{2} + \operatorname{re}{\left(z\right)} + \left(\operatorname{im}{\left(y\right)}\right)^{2} + 5 \right)}}{2} \right)} + \operatorname{re}{\left(y\right)} + 5\right)$$
=
2 2 20 - re(z) - 2*im (y) + 2*re (y) + 10*re(y) - I*im(z) + 10*I*im(y) + 4*I*im(y)*re(y)
$$2 \left(\operatorname{re}{\left(y\right)}\right)^{2} + 4 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 10 \operatorname{re}{\left(y\right)} - \operatorname{re}{\left(z\right)} - 2 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 10 i \operatorname{im}{\left(y\right)} - i \operatorname{im}{\left(z\right)} + 20$$
20 - re(z) - 2*im(y)^2 + 2*re(y)^2 + 10*re(y) - i*im(z) + 10*i*im(y) + 4*i*im(y)*re(y)