Sr Examen

Otras calculadoras

x^2+x*y-2*y^2-x+y=3 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src]
 2            2            
x  + x*y - 2*y  - x + y = 3
$$y + \left(- x + \left(- 2 y^{2} + \left(x^{2} + x y\right)\right)\right) = 3$$
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.

La ecuación se convierte de
$$y + \left(- x + \left(- 2 y^{2} + \left(x^{2} + x y\right)\right)\right) = 3$$
en
$$\left(y + \left(- x + \left(- 2 y^{2} + \left(x^{2} + x y\right)\right)\right)\right) - 3 = 0$$
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
$$a = 1$$
$$b = y - 1$$
$$c = - 2 y^{2} + y - 3$$
, entonces
D = b^2 - 4 * a * c = 

(-1 + y)^2 - 4 * (1) * (-3 + y - 2*y^2) = 12 + (-1 + y)^2 - 4*y + 8*y^2

La ecuación tiene dos raíces.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

o
$$x_{1} = - \frac{y}{2} + \frac{\sqrt{8 y^{2} - 4 y + \left(y - 1\right)^{2} + 12}}{2} + \frac{1}{2}$$
$$x_{2} = - \frac{y}{2} - \frac{\sqrt{8 y^{2} - 4 y + \left(y - 1\right)^{2} + 12}}{2} + \frac{1}{2}$$
Teorema de Cardano-Vieta
es ecuación cuadrática reducida
$$p x + q + x^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = y - 1$$
$$q = \frac{c}{a}$$
$$q = - 2 y^{2} + y - 3$$
Fórmulas de Cardano-Vieta
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1 - y$$
$$x_{1} x_{2} = - 2 y^{2} + y - 3$$
Gráfica
Respuesta rápida [src]
                   /              ______________________________________________________________________                                                                          \       ______________________________________________________________________                                                                          
                   |             /                                                                    2     /     /                                    2                    2   \\|      /                                                                    2     /     /                                    2                    2   \\
                   |          4 /                             2   /         2                    2   \      |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/||   4 /                             2   /         2                    2   \      |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|
                   |          \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *sin|--------------------------------------------------------------------||   \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *cos|--------------------------------------------------------------------|
     1   re(y)     |  im(y)                                                                                 \                                 2                                  /|                                                                                 \                                 2                                  /
x1 = - - ----- + I*|- ----- - ----------------------------------------------------------------------------------------------------------------------------------------------------| - ----------------------------------------------------------------------------------------------------------------------------------------------------
     2     2       \    2                                                                              2                                                                          /                                                                            2                                                                          
$$x_{1} = i \left(- \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) - \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{1}{2}$$
                   /              ______________________________________________________________________                                                                          \       ______________________________________________________________________                                                                          
                   |             /                                                                    2     /     /                                    2                    2   \\|      /                                                                    2     /     /                                    2                    2   \\
                   |          4 /                             2   /         2                    2   \      |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/||   4 /                             2   /         2                    2   \      |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|
                   |          \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *sin|--------------------------------------------------------------------||   \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *cos|--------------------------------------------------------------------|
     1   re(y)     |  im(y)                                                                                 \                                 2                                  /|                                                                                 \                                 2                                  /
x2 = - - ----- + I*|- ----- + ----------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------
     2     2       \    2                                                                              2                                                                          /                                                                            2                                                                          
$$x_{2} = i \left(\frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) + \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{1}{2}$$
x2 = i*(((18*re(y)*im(y) - 6*im(y))^2 + (9*re(y)^2 - 6*re(y) - 9*im(y)^2 + 13)^2)^(1/4)*sin(atan2(18*re(y)*im(y) - 6*im(y, 9*re(y)^2 - 6*re(y) - 9*im(y)^2 + 13)/2)/2 - im(y)/2) + ((18*re(y)*im(y) - 6*im(y))^2 + (9*re(y)^2 - 6*re(y) - 9*im(y)^2 + 13)^2)^(1/4)*cos(atan2(18*re(y)*im(y) - 6*im(y), 9*re(y)^2 - 6*re(y) - 9*im(y)^2 + 13)/2)/2 - re(y)/2 + 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\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/||   4 /                             2   /         2                    2   \      |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|                 |          4 /                             2   /         2                    2   \      |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/||   4 /                             2   /         2                    2   \      |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|
              |          \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *sin|--------------------------------------------------------------------||   \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *cos|--------------------------------------------------------------------|                 |          \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *sin|--------------------------------------------------------------------||   \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *cos|--------------------------------------------------------------------|
1   re(y)     |  im(y)                                                                                 \                                 2                                  /|                                                                                 \                                 2                                  /   1   re(y)     |  im(y)                                                                                 \                                 2                                  /|                                                                                 \                                 2                                  /
- - ----- + I*|- ----- - ----------------------------------------------------------------------------------------------------------------------------------------------------| - ---------------------------------------------------------------------------------------------------------------------------------------------------- + - - ----- + I*|- ----- + ----------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------
2     2       \    2                                                                              2                                                                          /                                                                            2                                                                             2     2       \    2                                                                              2                                                                          /                                                                            2                                                                          
$$\left(i \left(- \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) - \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{1}{2}\right) + \left(i \left(\frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) + \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{1}{2}\right)$$
=
              /              ______________________________________________________________________                                                                          \     /              ______________________________________________________________________                                                                          \
              |             /                                                                    2     /     /                                    2                    2   \\|     |             /                                                                    2     /     /                                    2                    2   \\|
              |          4 /                             2   /         2                    2   \      |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/||     |          4 /                             2   /         2                    2   \      |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/||
              |          \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *sin|--------------------------------------------------------------------||     |          \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *sin|--------------------------------------------------------------------||
              |  im(y)                                                                                 \                                 2                                  /|     |  im(y)                                                                                 \                                 2                                  /|
1 - re(y) + I*|- ----- + ----------------------------------------------------------------------------------------------------------------------------------------------------| + I*|- ----- - ----------------------------------------------------------------------------------------------------------------------------------------------------|
              \    2                                                                              2                                                                          /     \    2                                                                              2                                                                          /
$$i \left(- \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) + i \left(\frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) - \operatorname{re}{\left(y\right)} + 1$$
producto
/              /              ______________________________________________________________________                                                                          \       ______________________________________________________________________                                                                          \ /              /              ______________________________________________________________________                                                                          \       ______________________________________________________________________                                                                          \
|              |             /                                                                    2     /     /                                    2                    2   \\|      /                                                                    2     /     /                                    2                    2   \\| |              |             /                                                                    2     /     /                                    2                    2   \\|      /                                                                    2     /     /                                    2                    2   \\|
|              |          4 /                             2   /         2                    2   \      |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/||   4 /                             2   /         2                    2   \      |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/|| |              |          4 /                             2   /         2                    2   \      |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/||   4 /                             2   /         2                    2   \      |atan2\-6*im(y) + 18*im(y)*re(y), 13 - 9*im (y) - 6*re(y) + 9*re (y)/||
|              |          \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *sin|--------------------------------------------------------------------||   \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *cos|--------------------------------------------------------------------|| |              |          \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *sin|--------------------------------------------------------------------||   \/   (-6*im(y) + 18*im(y)*re(y))  + \13 - 9*im (y) - 6*re(y) + 9*re (y)/  *cos|--------------------------------------------------------------------||
|1   re(y)     |  im(y)                                                                                 \                                 2                                  /|                                                                                 \                                 2                                  /| |1   re(y)     |  im(y)                                                                                 \                                 2                                  /|                                                                                 \                                 2                                  /|
|- - ----- + I*|- ----- - ----------------------------------------------------------------------------------------------------------------------------------------------------| - ----------------------------------------------------------------------------------------------------------------------------------------------------|*|- - ----- + I*|- ----- + ----------------------------------------------------------------------------------------------------------------------------------------------------| + ----------------------------------------------------------------------------------------------------------------------------------------------------|
\2     2       \    2                                                                              2                                                                          /                                                                            2                                                                          / \2     2       \    2                                                                              2                                                                          /                                                                            2                                                                          /
$$\left(i \left(- \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) - \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{1}{2}\right) \left(i \left(\frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{im}{\left(y\right)}}{2}\right) + \frac{\sqrt[4]{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)}\right)^{2} + \left(9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(18 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 6 \operatorname{im}{\left(y\right)},9 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 6 \operatorname{re}{\left(y\right)} - 9 \left(\operatorname{im}{\left(y\right)}\right)^{2} + 13 \right)}}{2} \right)}}{2} - \frac{\operatorname{re}{\left(y\right)}}{2} + \frac{1}{2}\right)$$
=
         2          2                                       
-3 - 2*re (y) + 2*im (y) + I*im(y) - 4*I*im(y)*re(y) + re(y)
$$- 2 \left(\operatorname{re}{\left(y\right)}\right)^{2} - 4 i \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + \operatorname{re}{\left(y\right)} + 2 \left(\operatorname{im}{\left(y\right)}\right)^{2} + i \operatorname{im}{\left(y\right)} - 3$$
-3 - 2*re(y)^2 + 2*im(y)^2 + i*im(y) - 4*i*im(y)*re(y) + re(y)