Sr Examen
Otras calculadoras
-
¿Cómo usar?
- La ecuación:
-
Ecuación 8*x=2
-
Ecuación 3^x=81
-
Ecuación 5x+15=x-1
-
Ecuación 2*x^2-x+5=0
- Expresar {x} en función de y en la ecuación:
- 4*x-1*y=-3
- -11*x+9*y=-20
- 9*x+17*y=13
- -17*x+2*y=9
- Expresión:
- xyy
- Integral de d{x}:
- 1+y^2
- Gráfico de la función y =:
-
1+y^2
- Límite de la función:
- 1+y^2
-
Expresiones idénticas
- xyy= uno +y^ dos
- xyy es igual a 1 más y al cuadrado
- xyy es igual a uno más y en el grado dos
- xyy=1+y2
- xyy=1+y²
- xyy=1+y en el grado 2
-
Expresiones semejantes
- xyy=1-y^2
- (x+xy)^y
- x*y*(y-200)+b*y*(y+300)=(x+b)*(y+300)*(y-200)
- (1+e^x)yy^1=e^x
- 3*x^2*y-x*x*y*y-x*x*y=0
xyy=1+y^2 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$y x y = y^{2} + 1$$
en
$$y x y + \left(- y^{2} - 1\right) = 0$$
Es la ecuación de la forma
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = x - 1$$
$$b = 0$$
$$c = -1$$
, entonces
La ecuación tiene dos raíces.
o
$$y_{1} = \frac{\sqrt{4 x - 4}}{2 x - 2}$$
$$y_{2} = - \frac{\sqrt{4 x - 4}}{2 x - 2}$$
miembro izquierdo de la ecuación con el signo negativo.
La ecuación se convierte de
$$y x y = y^{2} + 1$$
en
$$y x y + \left(- y^{2} - 1\right) = 0$$
Es la ecuación de la forma
a*y^2 + b*y + c = 0
La ecuación cuadrática puede ser resuelta
con la ayuda del discriminante.
Las raíces de la ecuación cuadrática:
$$y_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$y_{2} = \frac{- \sqrt{D} - b}{2 a}$$
donde D = b^2 - 4*a*c es el discriminante.
Como
$$a = x - 1$$
$$b = 0$$
$$c = -1$$
, entonces
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-1 + x) * (-1) = -4 + 4*x
La ecuación tiene dos raíces.
y1 = (-b + sqrt(D)) / (2*a)
y2 = (-b - sqrt(D)) / (2*a)
o
$$y_{1} = \frac{\sqrt{4 x - 4}}{2 x - 2}$$
$$y_{2} = - \frac{\sqrt{4 x - 4}}{2 x - 2}$$
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
$$x y^{2} = y^{2} + 1$$
Коэффициент при y равен
$$x - 1$$
entonces son posibles los casos para x :
$$x < 1$$
$$x = 1$$
Consideremos todos los casos con detalles:
Con
$$x < 1$$
la ecuación será
$$- y^{2} - 1 = 0$$
su solución
no hay soluciones
Con
$$x = 1$$
la ecuación será
$$-1 = 0$$
su solución
no hay soluciones
$$x y^{2} = y^{2} + 1$$
Коэффициент при y равен
$$x - 1$$
entonces son posibles los casos para x :
$$x < 1$$
$$x = 1$$
Consideremos todos los casos con detalles:
Con
$$x < 1$$
la ecuación será
$$- y^{2} - 1 = 0$$
su solución
no hay soluciones
Con
$$x = 1$$
la ecuación será
$$-1 = 0$$
su solución
no hay soluciones
Teorema de Cardano-Vieta
reescribamos la ecuación
$$y x y = y^{2} + 1$$
de
$$a y^{2} + b y + c = 0$$
como ecuación cuadrática reducida
$$y^{2} + \frac{b y}{a} + \frac{c}{a} = 0$$
$$\frac{x y^{2} - y^{2} - 1}{x - 1} = 0$$
$$p y + q + y^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{x - 1}$$
Fórmulas de Cardano-Vieta
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = 0$$
$$y_{1} y_{2} = - \frac{1}{x - 1}$$
$$y x y = y^{2} + 1$$
de
$$a y^{2} + b y + c = 0$$
como ecuación cuadrática reducida
$$y^{2} + \frac{b y}{a} + \frac{c}{a} = 0$$
$$\frac{x y^{2} - y^{2} - 1}{x - 1} = 0$$
$$p y + q + y^{2} = 0$$
donde
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = - \frac{1}{x - 1}$$
Fórmulas de Cardano-Vieta
$$y_{1} + y_{2} = - p$$
$$y_{1} y_{2} = q$$
$$y_{1} + y_{2} = 0$$
$$y_{1} y_{2} = - \frac{1}{x - 1}$$
Gráfica
Suma y producto de raíces
[src]
suma
/ / -im(x) -1 + re(x) \\ / / -im(x) -1 + re(x) \\ / / -im(x) -1 + re(x) \\ / / -im(x) -1 + re(x) \\
_______________________________________________________ |atan2|----------------------, ----------------------|| _______________________________________________________ |atan2|----------------------, ----------------------|| _______________________________________________________ |atan2|----------------------, ----------------------|| _______________________________________________________ |atan2|----------------------, ----------------------||
/ 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||
/ (-1 + re(x)) im (x) | \(-1 + re(x)) + im (x) (-1 + re(x)) + im (x)/| / (-1 + re(x)) im (x) | \(-1 + re(x)) + im (x) (-1 + re(x)) + im (x)/| / (-1 + re(x)) im (x) | \(-1 + re(x)) + im (x) (-1 + re(x)) + im (x)/| / (-1 + re(x)) im (x) | \(-1 + re(x)) + im (x) (-1 + re(x)) + im (x)/|
- / ------------------------- + ------------------------- *cos|-----------------------------------------------------| - I* / ------------------------- + ------------------------- *sin|-----------------------------------------------------| + / ------------------------- + ------------------------- *cos|-----------------------------------------------------| + I* / ------------------------- + ------------------------- *sin|-----------------------------------------------------|
/ 2 2 \ 2 / / 2 2 \ 2 / / 2 2 \ 2 / / 2 2 \ 2 /
4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \
\/ \(-1 + re(x)) + im (x)/ \(-1 + re(x)) + im (x)/ \/ \(-1 + re(x)) + im (x)/ \(-1 + re(x)) + im (x)/ \/ \(-1 + re(x)) + im (x)/ \(-1 + re(x)) + im (x)/ \/ \(-1 + re(x)) + im (x)/ \(-1 + re(x)) + im (x)/
$$\left(- i \sqrt[4]{\frac{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\operatorname{re}{\left(x\right)} - 1}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\frac{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\operatorname{re}{\left(x\right)} - 1}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\frac{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\operatorname{re}{\left(x\right)} - 1}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\frac{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\operatorname{re}{\left(x\right)} - 1}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\right)$$
=
0
$$0$$
producto
/ / / -im(x) -1 + re(x) \\ / / -im(x) -1 + re(x) \\\ / / / -im(x) -1 + re(x) \\ / / -im(x) -1 + re(x) \\\ | _______________________________________________________ |atan2|----------------------, ----------------------|| _______________________________________________________ |atan2|----------------------, ----------------------||| | _______________________________________________________ |atan2|----------------------, ----------------------|| _______________________________________________________ |atan2|----------------------, ----------------------||| | / 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||| | / 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||| | / (-1 + re(x)) im (x) | \(-1 + re(x)) + im (x) (-1 + re(x)) + im (x)/| / (-1 + re(x)) im (x) | \(-1 + re(x)) + im (x) (-1 + re(x)) + im (x)/|| | / (-1 + re(x)) im (x) | \(-1 + re(x)) + im (x) (-1 + re(x)) + im (x)/| / (-1 + re(x)) im (x) | \(-1 + re(x)) + im (x) (-1 + re(x)) + im (x)/|| |- / ------------------------- + ------------------------- *cos|-----------------------------------------------------| - I* / ------------------------- + ------------------------- *sin|-----------------------------------------------------||*| / ------------------------- + ------------------------- *cos|-----------------------------------------------------| + I* / ------------------------- + ------------------------- *sin|-----------------------------------------------------|| | / 2 2 \ 2 / / 2 2 \ 2 /| | / 2 2 \ 2 / / 2 2 \ 2 /| | 4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \ | |4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \ | \ \/ \(-1 + re(x)) + im (x)/ \(-1 + re(x)) + im (x)/ \/ \(-1 + re(x)) + im (x)/ \(-1 + re(x)) + im (x)/ / \\/ \(-1 + re(x)) + im (x)/ \(-1 + re(x)) + im (x)/ \/ \(-1 + re(x)) + im (x)/ \(-1 + re(x)) + im (x)/ /
$$\left(- i \sqrt[4]{\frac{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\operatorname{re}{\left(x\right)} - 1}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\frac{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\operatorname{re}{\left(x\right)} - 1}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\frac{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\operatorname{re}{\left(x\right)} - 1}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\frac{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\operatorname{re}{\left(x\right)} - 1}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\right)$$
=
/ -im(x) -1 + re(x) \
I*atan2|----------------------, ----------------------|
| 2 2 2 2 |
\(-1 + re(x)) + im (x) (-1 + re(x)) + im (x)/
-e
----------------------------------------------------------
________________________
/ 2 2
\/ (-1 + re(x)) + im (x)
$$- \frac{e^{i \operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\operatorname{re}{\left(x\right)} - 1}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}}{\sqrt{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}}$$
-exp(i*atan2(-im(x)/((-1 + re(x))^2 + im(x)^2), (-1 + re(x))/((-1 + re(x))^2 + im(x)^2)))/sqrt((-1 + re(x))^2 + im(x)^2)
Respuesta rápida
[src]
/ / -im(x) -1 + re(x) \\ / / -im(x) -1 + re(x) \\
_______________________________________________________ |atan2|----------------------, ----------------------|| _______________________________________________________ |atan2|----------------------, ----------------------||
/ 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||
/ (-1 + re(x)) im (x) | \(-1 + re(x)) + im (x) (-1 + re(x)) + im (x)/| / (-1 + re(x)) im (x) | \(-1 + re(x)) + im (x) (-1 + re(x)) + im (x)/|
y1 = - / ------------------------- + ------------------------- *cos|-----------------------------------------------------| - I* / ------------------------- + ------------------------- *sin|-----------------------------------------------------|
/ 2 2 \ 2 / / 2 2 \ 2 /
4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \
\/ \(-1 + re(x)) + im (x)/ \(-1 + re(x)) + im (x)/ \/ \(-1 + re(x)) + im (x)/ \(-1 + re(x)) + im (x)/
$$y_{1} = - i \sqrt[4]{\frac{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\operatorname{re}{\left(x\right)} - 1}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\frac{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\operatorname{re}{\left(x\right)} - 1}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}$$
/ / -im(x) -1 + re(x) \\ / / -im(x) -1 + re(x) \\
_______________________________________________________ |atan2|----------------------, ----------------------|| _______________________________________________________ |atan2|----------------------, ----------------------||
/ 2 2 | | 2 2 2 2 || / 2 2 | | 2 2 2 2 ||
/ (-1 + re(x)) im (x) | \(-1 + re(x)) + im (x) (-1 + re(x)) + im (x)/| / (-1 + re(x)) im (x) | \(-1 + re(x)) + im (x) (-1 + re(x)) + im (x)/|
y2 = / ------------------------- + ------------------------- *cos|-----------------------------------------------------| + I* / ------------------------- + ------------------------- *sin|-----------------------------------------------------|
/ 2 2 \ 2 / / 2 2 \ 2 /
4 / / 2 2 \ / 2 2 \ 4 / / 2 2 \ / 2 2 \
\/ \(-1 + re(x)) + im (x)/ \(-1 + re(x)) + im (x)/ \/ \(-1 + re(x)) + im (x)/ \(-1 + re(x)) + im (x)/
$$y_{2} = i \sqrt[4]{\frac{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\operatorname{re}{\left(x\right)} - 1}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\frac{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}} + \frac{\left(\operatorname{im}{\left(x\right)}\right)^{2}}{\left(\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\operatorname{re}{\left(x\right)} - 1}{\left(\operatorname{re}{\left(x\right)} - 1\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}$$
y2 = i*((re(x) - 1)^2/((re(x) - 1)^2 + im(x)^2)^2 + im(x)^2/((re(x) - 1)^2 + im(x)^2)^2)^(1/4)*sin(atan2(-im(x)/((re(x) - 1)^2 + im(x)^2, (re(x) - 1)/((re(x) - 1)^2 + im(x)^2))/2) + ((re(x) - 1)^2/((re(x) - 1)^2 + im(x)^2)^2 + im(x)^2/((re(x) - 1)^2 + im(x)^2)^2)^(1/4)*cos(atan2(-im(x)/((re(x) - 1)^2 + im(x)^2), (re(x) - 1)/((re(x) - 1)^2 + im(x)^2))/2))