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sqrt(4x-4x^2-1)=y^2-x^2 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
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  /          2         2    2
\/  4*x - 4*x  - 1  = y  - x
(−4x2+4x)−1=−x2+y2\sqrt{\left(- 4 x^{2} + 4 x\right) - 1} = - x^{2} + y^{2}
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Respuesta rápida [src] 
       /        _________________________________________________                                                     \       _________________________________________________                                                     
       |       /                                               2     /     /                           2        2   \\|      /                                               2     /     /                           2        2   \\
       |    4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||   4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|
x1 = I*|1 - \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|-----------------------------------------------|| - \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *cos|-----------------------------------------------|
       \                                                             \                       2                       //                                                            \                       2                       /
x1=i(−(2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2)+1)−(2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24cos⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2)x_{1} = i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} 
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       |       /                                               2     /     /                           2        2   \\|      /                                               2     /     /                           2        2   \\
       |    4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||   4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|
x2 = I*|1 + \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|-----------------------------------------------|| + \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *cos|-----------------------------------------------|
       \                                                             \                       2                       //                                                            \                       2                       /
x2=i((2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2)+1)+(2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24cos⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2)x_{2} = i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} 
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       |        /                                              2     /     /                          2        2   \\|      /                                              2     /     /                          2        2   \\
       |     4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||   4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|
x3 = I*|-1 - \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|----------------------------------------------|| - \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *cos|----------------------------------------------|
       \                                                             \                      2                       //                                                           \                      2                       /
x3=i(−(2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2)−1)−(2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24cos⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2)x_{3} = i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} 
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       |        /                                              2     /     /                          2        2   \\|      /                                              2     /     /                          2        2   \\
       |     4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||   4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|
x4 = I*|-1 + \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|----------------------------------------------|| + \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *cos|----------------------------------------------|
       \                                                             \                      2                       //                                                           \                      2                       /
x4=i((2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2)−1)+(2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24cos⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2)x_{4} = i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} 
x4 = i*(((2*re(y)*im(y) + 1)^2 + (re(y)^2 - im(y)^2 - 1)^2)^(1/4)*sin(atan2(2*re(y)*im(y + 1, re(y)^2 - im(y)^2 - 1)/2) - 1) + ((2*re(y)*im(y) + 1)^2 + (re(y)^2 - im(y)^2 - 1)^2)^(1/4)*cos(atan2(2*re(y)*im(y) + 1, re(y)^2 - im(y)^2 - 1)/2))
Suma y producto de raíces [src] 
suma
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  |       /                                               2     /     /                           2        2   \\|      /                                               2     /     /                           2        2   \\     |       /                                               2     /     /                           2        2   \\|      /                                               2     /     /                           2        2   \\     |        /                                              2     /     /                          2        2   \\|      /                                              2     /     /                          2        2   \\     |        /                                              2     /     /                          2        2   \\|      /                                              2     /     /                          2        2   \\
  |    4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||   4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|     |    4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||   4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|     |     4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||   4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|     |     4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||   4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|
I*|1 - \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|-----------------------------------------------|| - \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *cos|-----------------------------------------------| + I*|1 + \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|-----------------------------------------------|| + \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *cos|-----------------------------------------------| + I*|-1 - \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|----------------------------------------------|| - \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *cos|----------------------------------------------| + I*|-1 + \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|----------------------------------------------|| + \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *cos|----------------------------------------------|
  \                                                             \                       2                       //                                                            \                       2                       /     \                                                             \                       2                       //                                                            \                       2                       /     \                                                             \                      2                       //                                                           \                      2                       /     \                                                             \                      2                       //                                                           \                      2                       /
(i((2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2)−1)+(2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24cos⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2))+((i(−(2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2)−1)−(2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24cos⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2))+((i(−(2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2)+1)−(2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24cos⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2))+(i((2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2)+1)+(2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24cos⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2))))\left(i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) + \left(\left(i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) + \left(\left(i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) + \left(i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right)\right)\right) 
=
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  |       /                                               2     /     /                           2        2   \\|     |       /                                               2     /     /                           2        2   \\|     |        /                                              2     /     /                          2        2   \\|     |        /                                              2     /     /                          2        2   \\|
  |    4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||     |    4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||     |     4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||     |     4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||
I*|1 + \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|-----------------------------------------------|| + I*|1 - \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|-----------------------------------------------|| + I*|-1 + \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|----------------------------------------------|| + I*|-1 - \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|----------------------------------------------||
  \                                                             \                       2                       //     \                                                             \                       2                       //     \                                                             \                      2                       //     \                                                             \                      2                       //
i(−(2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2)+1)+i((2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2)+1)+i(−(2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2)−1)+i((2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2)−1)i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) + i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) + i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) + i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) 
producto
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|  |    4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||   4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| |  |    4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||   4 /                      2   /       2        2   \      |atan2\-1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| |  |     4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||   4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/|| |  |     4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||   4 /                     2   /       2        2   \      |atan2\1 + 2*im(y)*re(y), -1 + re (y) - im (y)/||
|I*|1 - \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|-----------------------------------------------|| - \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *cos|-----------------------------------------------||*|I*|1 + \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|-----------------------------------------------|| + \/   (-1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *cos|-----------------------------------------------||*|I*|-1 - \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|----------------------------------------------|| - \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *cos|----------------------------------------------||*|I*|-1 + \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *sin|----------------------------------------------|| + \/   (1 + 2*im(y)*re(y))  + \-1 + re (y) - im (y)/  *cos|----------------------------------------------||
\  \                                                             \                       2                       //                                                            \                       2                       // \  \                                                             \                       2                       //                                                            \                       2                       // \  \                                                             \                      2                       //                                                           \                      2                       // \  \                                                             \                      2                       //                                                           \                      2                       //
(i(−(2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2)+1)−(2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24cos⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2))(i((2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2)+1)+(2re⁡(y)im⁡(y)−1)2+((re⁡(y))2−(im⁡(y))2−1)24cos⁡(atan2⁡(2re⁡(y)im⁡(y)−1,(re⁡(y))2−(im⁡(y))2−1)2))(i(−(2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2)−1)−(2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24cos⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2))(i((2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24sin⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2)−1)+(2re⁡(y)im⁡(y)+1)2+((re⁡(y))2−(im⁡(y))2−1)24cos⁡(atan2⁡(2re⁡(y)im⁡(y)+1,(re⁡(y))2−(im⁡(y))2−1)2))\left(i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) \left(i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} + 1\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} - 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) \left(i \left(- \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) - \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) \left(i \left(\sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)} - 1\right) + \sqrt[4]{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(2 \operatorname{re}{\left(y\right)} \operatorname{im}{\left(y\right)} + 1,\left(\operatorname{re}{\left(y\right)}\right)^{2} - \left(\operatorname{im}{\left(y\right)}\right)^{2} - 1 \right)}}{2} \right)}\right) 
=
      4        4          2      2            3                  3         
1 + im (y) + re (y) - 6*im (y)*re (y) - 4*I*im (y)*re(y) + 4*I*re (y)*im(y)
(re⁡(y))4+4i(re⁡(y))3im⁡(y)−6(re⁡(y))2(im⁡(y))2−4ire⁡(y)(im⁡(y))3+(im⁡(y))4+1\left(\operatorname{re}{\left(y\right)}\right)^{4} + 4 i \left(\operatorname{re}{\left(y\right)}\right)^{3} \operatorname{im}{\left(y\right)} - 6 \left(\operatorname{re}{\left(y\right)}\right)^{2} \left(\operatorname{im}{\left(y\right)}\right)^{2} - 4 i \operatorname{re}{\left(y\right)} \left(\operatorname{im}{\left(y\right)}\right)^{3} + \left(\operatorname{im}{\left(y\right)}\right)^{4} + 1 
1 + im(y)^4 + re(y)^4 - 6*im(y)^2*re(y)^2 - 4*i*im(y)^3*re(y) + 4*i*re(y)^3*im(y)
    © Sr Examen – Калькулятор