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xyy=1+y^2 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
             2
x*y*y = 1 + y
yxy=y2+1y x y = y^{2} + 1
Simplificar
Solución detallada
Transportemos el miembro derecho de la ecuación al
miembro izquierdo de la ecuación con el signo negativo.

La ecuación se convierte de
yxy=y2+1y x y = y^{2} + 1
en
yxy+(−y2−1)=0y 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:
y1=D−b2ay_{1} = \frac{\sqrt{D} - b}{2 a}
y2=−D−b2ay_{2} = \frac{- \sqrt{D} - b}{2 a}
donde D = b^2 - 4*a*c es el discriminante.
Como
a=x−1a = x - 1
b=0b = 0
c=−1c = -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
y1=4x−42x−2y_{1} = \frac{\sqrt{4 x - 4}}{2 x - 2}
y2=−4x−42x−2y_{2} = - \frac{\sqrt{4 x - 4}}{2 x - 2}
Resolución de la ecuación paramétrica
Se da la ecuación con parámetro:
xy2=y2+1x y^{2} = y^{2} + 1
Коэффициент при y равен
x−1x - 1
entonces son posibles los casos para x :
x<1x < 1
x=1x = 1
Consideremos todos los casos con detalles:
Con
x<1x < 1
la ecuación será
−y2−1=0- y^{2} - 1 = 0
su solución
no hay soluciones
Con
x=1x = 1
la ecuación será
−1=0-1 = 0
su solución
no hay soluciones
Teorema de Cardano-Vieta
reescribamos la ecuación
yxy=y2+1y x y = y^{2} + 1
de
ay2+by+c=0a y^{2} + b y + c = 0
como ecuación cuadrática reducida
y2+bya+ca=0y^{2} + \frac{b y}{a} + \frac{c}{a} = 0
xy2−y2−1x−1=0\frac{x y^{2} - y^{2} - 1}{x - 1} = 0
py+q+y2=0p y + q + y^{2} = 0
donde
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=−1x−1q = - \frac{1}{x - 1}
Fórmulas de Cardano-Vieta
y1+y2=−py_{1} + y_{2} = - p
y1y2=qy_{1} y_{2} = q
y1+y2=0y_{1} + y_{2} = 0
y1y2=−1x−1y_{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)/
(−i(re⁡(x)−1)2((re⁡(x)−1)2+(im⁡(x))2)2+(im⁡(x))2((re⁡(x)−1)2+(im⁡(x))2)24sin⁡(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)24cos⁡(atan2⁡(−im⁡(x)(re⁡(x)−1)2+(im⁡(x))2,re⁡(x)−1(re⁡(x)−1)2+(im⁡(x))2)2))+(i(re⁡(x)−1)2((re⁡(x)−1)2+(im⁡(x))2)2+(im⁡(x))2((re⁡(x)−1)2+(im⁡(x))2)24sin⁡(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)24cos⁡(atan2⁡(−im⁡(x)(re⁡(x)−1)2+(im⁡(x))2,re⁡(x)−1(re⁡(x)−1)2+(im⁡(x))2)2))\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
00 
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)/                                                             /
(−i(re⁡(x)−1)2((re⁡(x)−1)2+(im⁡(x))2)2+(im⁡(x))2((re⁡(x)−1)2+(im⁡(x))2)24sin⁡(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)24cos⁡(atan2⁡(−im⁡(x)(re⁡(x)−1)2+(im⁡(x))2,re⁡(x)−1(re⁡(x)−1)2+(im⁡(x))2)2))(i(re⁡(x)−1)2((re⁡(x)−1)2+(im⁡(x))2)2+(im⁡(x))2((re⁡(x)−1)2+(im⁡(x))2)24sin⁡(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)24cos⁡(atan2⁡(−im⁡(x)(re⁡(x)−1)2+(im⁡(x))2,re⁡(x)−1(re⁡(x)−1)2+(im⁡(x))2)2))\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)
−eiatan2⁡(−im⁡(x)(re⁡(x)−1)2+(im⁡(x))2,re⁡(x)−1(re⁡(x)−1)2+(im⁡(x))2)(re⁡(x)−1)2+(im⁡(x))2- \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)/
y1=−i(re⁡(x)−1)2((re⁡(x)−1)2+(im⁡(x))2)2+(im⁡(x))2((re⁡(x)−1)2+(im⁡(x))2)24sin⁡(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)24cos⁡(atan2⁡(−im⁡(x)(re⁡(x)−1)2+(im⁡(x))2,re⁡(x)−1(re⁡(x)−1)2+(im⁡(x))2)2)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)/
y2=i(re⁡(x)−1)2((re⁡(x)−1)2+(im⁡(x))2)2+(im⁡(x))2((re⁡(x)−1)2+(im⁡(x))2)24sin⁡(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)24cos⁡(atan2⁡(−im⁡(x)(re⁡(x)−1)2+(im⁡(x))2,re⁡(x)−1(re⁡(x)−1)2+(im⁡(x))2)2)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))
    © Sr Examen – Калькулятор