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- La ecuación:
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Ecuación x^2-4x+5=0
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Ecuación 9-4x=3x-40
- Ecuación y+x-4=0
-
Ecuación (x-4)^2-x^2=0
- Expresar {x} en función de y en la ecuación:
- -18*x-2*y=9
- 4*x+2*y=5
- -9*x+1*y=3
- 19*x-12*y=16
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Expresiones idénticas
- cuatro *(((uno /sqrt(dos))*x-(uno /sqrt(dos))*y)- dos *sqrt(dos))^ dos - dos *(((uno /sqrt(dos))*x+(uno /sqrt(dos))*y)-sqrt(dos))= cero
- 4 multiplicar por (((1 dividir por raíz cuadrada de (2)) multiplicar por x menos (1 dividir por raíz cuadrada de (2)) multiplicar por y) menos 2 multiplicar por raíz cuadrada de (2)) al cuadrado menos 2 multiplicar por (((1 dividir por raíz cuadrada de (2)) multiplicar por x más (1 dividir por raíz cuadrada de (2)) multiplicar por y) menos raíz cuadrada de (2)) es igual a 0
- cuatro multiplicar por (((uno dividir por raíz cuadrada de (dos)) multiplicar por x menos (uno dividir por raíz cuadrada de (dos)) multiplicar por y) menos dos multiplicar por raíz cuadrada de (dos)) en el grado dos menos dos multiplicar por (((uno dividir por raíz cuadrada de (dos)) multiplicar por x más (uno dividir por raíz cuadrada de (dos)) multiplicar por y) menos raíz cuadrada de (dos)) es igual a cero
- 4*(((1/√(2))*x-(1/√(2))*y)-2*√(2))^2-2*(((1/√(2))*x+(1/√(2))*y)-√(2))=0
- 4*(((1/sqrt(2))*x-(1/sqrt(2))*y)-2*sqrt(2))2-2*(((1/sqrt(2))*x+(1/sqrt(2))*y)-sqrt(2))=0
- 4*1/sqrt2*x-1/sqrt2*y-2*sqrt22-2*1/sqrt2*x+1/sqrt2*y-sqrt2=0
- 4*(((1/sqrt(2))*x-(1/sqrt(2))*y)-2*sqrt(2))²-2*(((1/sqrt(2))*x+(1/sqrt(2))*y)-sqrt(2))=0
- 4*(((1/sqrt(2))*x-(1/sqrt(2))*y)-2*sqrt(2)) en el grado 2-2*(((1/sqrt(2))*x+(1/sqrt(2))*y)-sqrt(2))=0
- 4(((1/sqrt(2))x-(1/sqrt(2))y)-2sqrt(2))^2-2(((1/sqrt(2))x+(1/sqrt(2))y)-sqrt(2))=0
- 4(((1/sqrt(2))x-(1/sqrt(2))y)-2sqrt(2))2-2(((1/sqrt(2))x+(1/sqrt(2))y)-sqrt(2))=0
- 41/sqrt2x-1/sqrt2y-2sqrt22-21/sqrt2x+1/sqrt2y-sqrt2=0
- 41/sqrt2x-1/sqrt2y-2sqrt2^2-21/sqrt2x+1/sqrt2y-sqrt2=0
- 4*(((1/sqrt(2))*x-(1/sqrt(2))*y)-2*sqrt(2))^2-2*(((1/sqrt(2))*x+(1/sqrt(2))*y)-sqrt(2))=O
- 4*(((1 dividir por sqrt(2))*x-(1 dividir por sqrt(2))*y)-2*sqrt(2))^2-2*(((1 dividir por sqrt(2))*x+(1 dividir por sqrt(2))*y)-sqrt(2))=0
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Expresiones semejantes
- 4*(((1/sqrt(2))*x+(1/sqrt(2))*y)-2*sqrt(2))^2-2*(((1/sqrt(2))*x+(1/sqrt(2))*y)-sqrt(2))=0
- 4*(((1/sqrt(2))*x-(1/sqrt(2))*y)-2*sqrt(2))^2+2*(((1/sqrt(2))*x+(1/sqrt(2))*y)-sqrt(2))=0
- 4*(((1/sqrt(2))*x-(1/sqrt(2))*y)-2*sqrt(2))^2-2*(((1/sqrt(2))*x+(1/sqrt(2))*y)+sqrt(2))=0
- 4*(((1/sqrt(2))*x-(1/sqrt(2))*y)-2*sqrt(2))^2-2*(((1/sqrt(2))*x-(1/sqrt(2))*y)-sqrt(2))=0
- 4*(((1/sqrt(2))*x-(1/sqrt(2))*y)+2*sqrt(2))^2-2*(((1/sqrt(2))*x+(1/sqrt(2))*y)-sqrt(2))=0
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x)=1
- sqrt(x^2-5x+1)=sqrt(x-4)
- sqrt(12+x)-sqrt(1-x)=1
- sqrt(x)=5
- sqrt(6+x-x^2)=1-x
- Raíz cuadrada sqrt
- sqrt(x)=1
- sqrt(x^2-5x+1)=sqrt(x-4)
- sqrt(12+x)-sqrt(1-x)=1
- sqrt(x)=5
- sqrt(6+x-x^2)=1-x
- Raíz cuadrada sqrt
- sqrt(x)=1
- sqrt(x^2-5x+1)=sqrt(x-4)
- sqrt(12+x)-sqrt(1-x)=1
- sqrt(x)=5
- sqrt(6+x-x^2)=1-x
- Raíz cuadrada sqrt
- sqrt(x)=1
- sqrt(x^2-5x+1)=sqrt(x-4)
- sqrt(12+x)-sqrt(1-x)=1
- sqrt(x)=5
- sqrt(6+x-x^2)=1-x
- Raíz cuadrada sqrt
- sqrt(x)=1
- sqrt(x^2-5x+1)=sqrt(x-4)
- sqrt(12+x)-sqrt(1-x)=1
- sqrt(x)=5
- sqrt(6+x-x^2)=1-x
- Raíz cuadrada sqrt
- sqrt(x)=1
- sqrt(x^2-5x+1)=sqrt(x-4)
- sqrt(12+x)-sqrt(1-x)=1
- sqrt(x)=5
- sqrt(6+x-x^2)=1-x
4*(((1/sqrt(2))*x-(1/sqrt(2))*y)-2*sqrt(2))^2-2*(((1/sqrt(2))*x+(1/sqrt(2))*y)-sqrt(2))=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
2 / x y ___\ / x y ___\ 4*|----- - ----- - 2*\/ 2 | - 2*|----- + ----- - \/ 2 | = 0 | ___ ___ | | ___ ___ | \\/ 2 \/ 2 / \\/ 2 \/ 2 /
$$4 \left(\left(\frac{x}{\sqrt{2}} - \frac{y}{\sqrt{2}}\right) - 2 \sqrt{2}\right)^{2} - 2 \left(\left(\frac{x}{\sqrt{2}} + \frac{y}{\sqrt{2}}\right) - \sqrt{2}\right) = 0$$
Solución detallada
Abramos la expresión en la ecuación
$$4 \left(\left(\frac{x}{\sqrt{2}} - \frac{y}{\sqrt{2}}\right) - 2 \sqrt{2}\right)^{2} - 2 \left(\left(\frac{x}{\sqrt{2}} + \frac{y}{\sqrt{2}}\right) - \sqrt{2}\right) = 0$$
Obtenemos la ecuación cuadrática
$$2 x^{2} - 4 x y - 16 \frac{\sqrt{2}}{2} \sqrt{2} x - \sqrt{2} x + 2 y^{2} - \sqrt{2} y + 16 \frac{\sqrt{2}}{2} \sqrt{2} y + 2 \sqrt{2} + 32 = 0$$
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
$$a = 2$$
$$b = - 4 y - 16 - \sqrt{2}$$
$$c = 2 y^{2} - \sqrt{2} y + 16 y + 2 \sqrt{2} + 32$$
, entonces
La ecuación tiene dos raíces.
o
$$x_{1} = y + \frac{\sqrt{- 16 y^{2} - 128 y + 8 \sqrt{2} y + \left(- 4 y - 16 - \sqrt{2}\right)^{2} - 256 - 16 \sqrt{2}}}{4} + \frac{\sqrt{2}}{4} + 4$$
$$x_{2} = y - \frac{\sqrt{- 16 y^{2} - 128 y + 8 \sqrt{2} y + \left(- 4 y - 16 - \sqrt{2}\right)^{2} - 256 - 16 \sqrt{2}}}{4} + \frac{\sqrt{2}}{4} + 4$$
$$4 \left(\left(\frac{x}{\sqrt{2}} - \frac{y}{\sqrt{2}}\right) - 2 \sqrt{2}\right)^{2} - 2 \left(\left(\frac{x}{\sqrt{2}} + \frac{y}{\sqrt{2}}\right) - \sqrt{2}\right) = 0$$
Obtenemos la ecuación cuadrática
$$2 x^{2} - 4 x y - 16 \frac{\sqrt{2}}{2} \sqrt{2} x - \sqrt{2} x + 2 y^{2} - \sqrt{2} y + 16 \frac{\sqrt{2}}{2} \sqrt{2} y + 2 \sqrt{2} + 32 = 0$$
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
$$a = 2$$
$$b = - 4 y - 16 - \sqrt{2}$$
$$c = 2 y^{2} - \sqrt{2} y + 16 y + 2 \sqrt{2} + 32$$
, entonces
D = b^2 - 4 * a * c =
(-16 - sqrt(2) - 4*y)^2 - 4 * (2) * (32 + 2*sqrt(2) + 2*y^2 + 16*y - y*sqrt(2)) = -256 + (-16 - sqrt(2) - 4*y)^2 - 128*y - 16*sqrt(2) - 16*y^2 + 8*y*sqrt(2)
La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
o
$$x_{1} = y + \frac{\sqrt{- 16 y^{2} - 128 y + 8 \sqrt{2} y + \left(- 4 y - 16 - \sqrt{2}\right)^{2} - 256 - 16 \sqrt{2}}}{4} + \frac{\sqrt{2}}{4} + 4$$
$$x_{2} = y - \frac{\sqrt{- 16 y^{2} - 128 y + 8 \sqrt{2} y + \left(- 4 y - 16 - \sqrt{2}\right)^{2} - 256 - 16 \sqrt{2}}}{4} + \frac{\sqrt{2}}{4} + 4$$
Gráfica
Respuesta rápida
[src]
/ _______________________________________________ \ _______________________________________________
| / 2 / / ___ ___ ___ \\ | / 2 / / ___ ___ ___ \\
| 4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/| | 4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/|
___ | \/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *sin|----------------------------------------------------| | \/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *cos|----------------------------------------------------|
\/ 2 | \ 2 / | \ 2 /
x1 = 4 + ----- + I*|- ------------------------------------------------------------------------------------------------------------- + im(y)| - ------------------------------------------------------------------------------------------------------------- + re(y)
4 \ 4 / 4
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{im}{\left(y\right)}\right) - \frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{re}{\left(y\right)} + \frac{\sqrt{2}}{4} + 4$$
/ _______________________________________________ \ _______________________________________________
| / 2 / / ___ ___ ___ \\ | / 2 / / ___ ___ ___ \\
|4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/| | 4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/|
___ |\/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *sin|----------------------------------------------------| | \/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *cos|----------------------------------------------------|
\/ 2 | \ 2 / | \ 2 /
x2 = 4 + ----- + I*|------------------------------------------------------------------------------------------------------------- + im(y)| + ------------------------------------------------------------------------------------------------------------- + re(y)
4 \ 4 / 4
$$x_{2} = i \left(\frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{im}{\left(y\right)}\right) + \frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{re}{\left(y\right)} + \frac{\sqrt{2}}{4} + 4$$
x2 = i*(((16*sqrt(2)*re(y) + 2 + 16*sqrt(2))^2 + 512*im(y)^2)^(1/4)*sin(atan2(16*sqrt(2)*im(y, 16*sqrt(2)*re(y) + 2 + 16*sqrt(2))/2)/4 + im(y)) + ((16*sqrt(2)*re(y) + 2 + 16*sqrt(2))^2 + 512*im(y)^2)^(1/4)*cos(atan2(16*sqrt(2)*im(y), 16*sqrt(2)*re(y) + 2 + 16*sqrt(2))/2)/4 + re(y) + sqrt(2)/4 + 4)
Suma y producto de raíces
[src]
suma
/ _______________________________________________ \ _______________________________________________ / _______________________________________________ \ _______________________________________________
| / 2 / / ___ ___ ___ \\ | / 2 / / ___ ___ ___ \\ | / 2 / / ___ ___ ___ \\ | / 2 / / ___ ___ ___ \\
| 4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/| | 4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/| |4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/| | 4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/|
___ | \/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *sin|----------------------------------------------------| | \/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *cos|----------------------------------------------------| ___ |\/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *sin|----------------------------------------------------| | \/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *cos|----------------------------------------------------|
\/ 2 | \ 2 / | \ 2 / \/ 2 | \ 2 / | \ 2 /
4 + ----- + I*|- ------------------------------------------------------------------------------------------------------------- + im(y)| - ------------------------------------------------------------------------------------------------------------- + re(y) + 4 + ----- + I*|------------------------------------------------------------------------------------------------------------- + im(y)| + ------------------------------------------------------------------------------------------------------------- + re(y)
4 \ 4 / 4 4 \ 4 / 4
$$\left(i \left(- \frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{im}{\left(y\right)}\right) - \frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{re}{\left(y\right)} + \frac{\sqrt{2}}{4} + 4\right) + \left(i \left(\frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{im}{\left(y\right)}\right) + \frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{re}{\left(y\right)} + \frac{\sqrt{2}}{4} + 4\right)$$
=
/ _______________________________________________ \ / _______________________________________________ \
| / 2 / / ___ ___ ___ \\ | | / 2 / / ___ ___ ___ \\ |
| 4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/| | |4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/| |
___ | \/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *sin|----------------------------------------------------| | |\/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *sin|----------------------------------------------------| |
\/ 2 | \ 2 / | | \ 2 / |
8 + ----- + 2*re(y) + I*|- ------------------------------------------------------------------------------------------------------------- + im(y)| + I*|------------------------------------------------------------------------------------------------------------- + im(y)|
2 \ 4 / \ 4 /
$$i \left(- \frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{im}{\left(y\right)}\right) + i \left(\frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{im}{\left(y\right)}\right) + 2 \operatorname{re}{\left(y\right)} + \frac{\sqrt{2}}{2} + 8$$
producto
/ / _______________________________________________ \ _______________________________________________ \ / / _______________________________________________ \ _______________________________________________ \ | | / 2 / / ___ ___ ___ \\ | / 2 / / ___ ___ ___ \\ | | | / 2 / / ___ ___ ___ \\ | / 2 / / ___ ___ ___ \\ | | | 4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/| | 4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/| | | |4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/| | 4 / / ___ ___ \ 2 |atan2\16*\/ 2 *im(y), 2 + 16*\/ 2 + 16*\/ 2 *re(y)/| | | ___ | \/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *sin|----------------------------------------------------| | \/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *cos|----------------------------------------------------| | | ___ |\/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *sin|----------------------------------------------------| | \/ \2 + 16*\/ 2 + 16*\/ 2 *re(y)/ + 512*im (y) *cos|----------------------------------------------------| | | \/ 2 | \ 2 / | \ 2 / | | \/ 2 | \ 2 / | \ 2 / | |4 + ----- + I*|- ------------------------------------------------------------------------------------------------------------- + im(y)| - ------------------------------------------------------------------------------------------------------------- + re(y)|*|4 + ----- + I*|------------------------------------------------------------------------------------------------------------- + im(y)| + ------------------------------------------------------------------------------------------------------------- + re(y)| \ 4 \ 4 / 4 / \ 4 \ 4 / 4 /
$$\left(i \left(- \frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{im}{\left(y\right)}\right) - \frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{re}{\left(y\right)} + \frac{\sqrt{2}}{4} + 4\right) \left(i \left(\frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{im}{\left(y\right)}\right) + \frac{\sqrt[4]{\left(16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2}\right)^{2} + 512 \left(\operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(16 \sqrt{2} \operatorname{im}{\left(y\right)},16 \sqrt{2} \operatorname{re}{\left(y\right)} + 2 + 16 \sqrt{2} \right)}}{2} \right)}}{4} + \operatorname{re}{\left(y\right)} + \frac{\sqrt{2}}{4} + 4\right)$$
=
___ ___
___ 2 2 \/ 2 *re(y) I*\/ 2 *im(y)
16 + \/ 2 + re (y) - im (y) + 8*re(y) + 8*I*im(y) - ----------- + 2*I*im(y)*re(y) - -------------
2 2
$$\left(\operatorname{re}{\left(y\right)}\right)^{2} + 2 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - \frac{\sqrt{2} \operatorname{re}{\left(y\right)}}{2} + 8 \operatorname{re}{\left(y\right)} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - \frac{\sqrt{2} i \operatorname{im}{\left(y\right)}}{2} + 8 i \operatorname{im}{\left(y\right)} + \sqrt{2} + 16$$
16 + sqrt(2) + re(y)^2 - im(y)^2 + 8*re(y) + 8*i*im(y) - sqrt(2)*re(y)/2 + 2*i*im(y)*re(y) - i*sqrt(2)*im(y)/2