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4sqtr(x)-(a+5)2sqrt(x)+4a+4=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
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4*\/ x  - (a + 5)*2*\/ x  + 4*a + 4 = 0
$$\left(4 a + \left(- \sqrt{x} 2 \left(a + 5\right) + 4 \sqrt{x}\right)\right) + 4 = 0$$
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Respuesta rápida [src] 
       /      _________________ /         _________________                         \                                    _________________ /        _________________                         \                          \   /        _________________                         \ /         _________________                         \                                   _________________                                                     
       |   4 /   2        2     |      4 /   2        2        /atan2(im(x), re(x))\|    /atan2(im(x), re(x))\        4 /   2        2     |     4 /   2        2        /atan2(im(x), re(x))\|    /atan2(im(x), re(x))\ |   |     4 /   2        2        /atan2(im(x), re(x))\| |      4 /   2        2        /atan2(im(x), re(x))\|                                  /   2        2        2/atan2(im(x), re(x))\                           
       |   \/  im (x) + re (x) *|2 - 3*\/  im (x) + re (x) *cos|-------------------||*sin|-------------------|      3*\/  im (x) + re (x) *|-2 + \/  im (x) + re (x) *cos|-------------------||*sin|-------------------| |   |-2 + \/  im (x) + re (x) *cos|-------------------||*|2 - 3*\/  im (x) + re (x) *cos|-------------------||                              3*\/  im (x) + re (x) *sin |-------------------|                           
       |                        \                              \         2         //    \         2         /                             \                             \         2         //    \         2         / |   \                             \         2         // \                              \         2         //                                                         \         2         /                           
a1 = I*|- ------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------
       |                                                      2                                                                                                        2                                                 |                                                         2                                                                                                          2                                                 
       |  /        _________________                         \       _________________                             /        _________________                         \       _________________                          |     /        _________________                         \       _________________                               /        _________________                         \       _________________                          
       |  |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\   |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\|     |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\     |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\
       |  |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------|   |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------||     |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------|     |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------|
       \  \                             \         2         //                             \         2         /   \                             \         2         //                             \         2         //     \                             \         2         //                             \         2         /     \                             \         2         //                             \         2         /
$$a_{1} = \frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} + i \left(- \frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} - \frac{3 \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) - \frac{3 \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$ 
a1 = (-3*(re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x, re(x))/2) + 2)*((re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) - 2)/(((re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) - 2)^2 + sqrt(re(x)^2 + im(x)^2)*sin(atan2(im(x), re(x))/2)^2) + i*(-(-3*(re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) + 2)*(re(x)^2 + im(x)^2)^(1/4)*sin(atan2(im(x), re(x))/2)/(((re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) - 2)^2 + sqrt(re(x)^2 + im(x)^2)*sin(atan2(im(x), re(x))/2)^2) - 3*((re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) - 2)*(re(x)^2 + im(x)^2)^(1/4)*sin(atan2(im(x), re(x))/2)/(((re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) - 2)^2 + sqrt(re(x)^2 + im(x)^2)*sin(atan2(im(x), re(x))/2)^2)) - 3*sqrt(re(x)^2 + im(x)^2)*sin(atan2(im(x), re(x))/2)^2/(((re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) - 2)^2 + sqrt(re(x)^2 + im(x)^2)*sin(atan2(im(x), re(x))/2)^2))
Suma y producto de raíces [src] 
suma
  /      _________________ /         _________________                         \                                    _________________ /        _________________                         \                          \   /        _________________                         \ /         _________________                         \                                   _________________                                                     
  |   4 /   2        2     |      4 /   2        2        /atan2(im(x), re(x))\|    /atan2(im(x), re(x))\        4 /   2        2     |     4 /   2        2        /atan2(im(x), re(x))\|    /atan2(im(x), re(x))\ |   |     4 /   2        2        /atan2(im(x), re(x))\| |      4 /   2        2        /atan2(im(x), re(x))\|                                  /   2        2        2/atan2(im(x), re(x))\                           
  |   \/  im (x) + re (x) *|2 - 3*\/  im (x) + re (x) *cos|-------------------||*sin|-------------------|      3*\/  im (x) + re (x) *|-2 + \/  im (x) + re (x) *cos|-------------------||*sin|-------------------| |   |-2 + \/  im (x) + re (x) *cos|-------------------||*|2 - 3*\/  im (x) + re (x) *cos|-------------------||                              3*\/  im (x) + re (x) *sin |-------------------|                           
  |                        \                              \         2         //    \         2         /                             \                             \         2         //    \         2         / |   \                             \         2         // \                              \         2         //                                                         \         2         /                           
I*|- ------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------
  |                                                      2                                                                                                        2                                                 |                                                         2                                                                                                          2                                                 
  |  /        _________________                         \       _________________                             /        _________________                         \       _________________                          |     /        _________________                         \       _________________                               /        _________________                         \       _________________                          
  |  |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\   |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\|     |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\     |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\
  |  |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------|   |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------||     |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------|     |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------|
  \  \                             \         2         //                             \         2         /   \                             \         2         //                             \         2         //     \                             \         2         //                             \         2         /     \                             \         2         //                             \         2         /
$$\frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} + i \left(- \frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} - \frac{3 \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) - \frac{3 \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$ 
=
  /      _________________ /         _________________                         \                                    _________________ /        _________________                         \                          \   /        _________________                         \ /         _________________                         \                                   _________________                                                     
  |   4 /   2        2     |      4 /   2        2        /atan2(im(x), re(x))\|    /atan2(im(x), re(x))\        4 /   2        2     |     4 /   2        2        /atan2(im(x), re(x))\|    /atan2(im(x), re(x))\ |   |     4 /   2        2        /atan2(im(x), re(x))\| |      4 /   2        2        /atan2(im(x), re(x))\|                                  /   2        2        2/atan2(im(x), re(x))\                           
  |   \/  im (x) + re (x) *|2 - 3*\/  im (x) + re (x) *cos|-------------------||*sin|-------------------|      3*\/  im (x) + re (x) *|-2 + \/  im (x) + re (x) *cos|-------------------||*sin|-------------------| |   |-2 + \/  im (x) + re (x) *cos|-------------------||*|2 - 3*\/  im (x) + re (x) *cos|-------------------||                              3*\/  im (x) + re (x) *sin |-------------------|                           
  |                        \                              \         2         //    \         2         /                             \                             \         2         //    \         2         / |   \                             \         2         // \                              \         2         //                                                         \         2         /                           
I*|- ------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------
  |                                                      2                                                                                                        2                                                 |                                                         2                                                                                                          2                                                 
  |  /        _________________                         \       _________________                             /        _________________                         \       _________________                          |     /        _________________                         \       _________________                               /        _________________                         \       _________________                          
  |  |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\   |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\|     |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\     |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\
  |  |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------|   |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------||     |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------|     |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------|
  \  \                             \         2         //                             \         2         /   \                             \         2         //                             \         2         //     \                             \         2         //                             \         2         /     \                             \         2         //                             \         2         /
$$\frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} + i \left(- \frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} - \frac{3 \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) - \frac{3 \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$ 
producto
  /      _________________ /         _________________                         \                                    _________________ /        _________________                         \                          \   /        _________________                         \ /         _________________                         \                                   _________________                                                     
  |   4 /   2        2     |      4 /   2        2        /atan2(im(x), re(x))\|    /atan2(im(x), re(x))\        4 /   2        2     |     4 /   2        2        /atan2(im(x), re(x))\|    /atan2(im(x), re(x))\ |   |     4 /   2        2        /atan2(im(x), re(x))\| |      4 /   2        2        /atan2(im(x), re(x))\|                                  /   2        2        2/atan2(im(x), re(x))\                           
  |   \/  im (x) + re (x) *|2 - 3*\/  im (x) + re (x) *cos|-------------------||*sin|-------------------|      3*\/  im (x) + re (x) *|-2 + \/  im (x) + re (x) *cos|-------------------||*sin|-------------------| |   |-2 + \/  im (x) + re (x) *cos|-------------------||*|2 - 3*\/  im (x) + re (x) *cos|-------------------||                              3*\/  im (x) + re (x) *sin |-------------------|                           
  |                        \                              \         2         //    \         2         /                             \                             \         2         //    \         2         / |   \                             \         2         // \                              \         2         //                                                         \         2         /                           
I*|- ------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------
  |                                                      2                                                                                                        2                                                 |                                                         2                                                                                                          2                                                 
  |  /        _________________                         \       _________________                             /        _________________                         \       _________________                          |     /        _________________                         \       _________________                               /        _________________                         \       _________________                          
  |  |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\   |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\|     |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\     |     4 /   2        2        /atan2(im(x), re(x))\|      /   2        2        2/atan2(im(x), re(x))\
  |  |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------|   |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------||     |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------|     |-2 + \/  im (x) + re (x) *cos|-------------------||  + \/  im (x) + re (x) *sin |-------------------|
  \  \                             \         2         //                             \         2         /   \                             \         2         //                             \         2         //     \                             \         2         //                             \         2         /     \                             \         2         //                             \         2         /
$$\frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} + i \left(- \frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} - \frac{3 \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) - \frac{3 \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$ 
=
          _________________        _________________                                   _________________                         
         /   2        2         4 /   2        2        /atan2(im(x), re(x))\       4 /   2        2        /atan2(im(x), re(x))\
-4 - 3*\/  im (x) + re (x)  + 8*\/  im (x) + re (x) *cos|-------------------| + 4*I*\/  im (x) + re (x) *sin|-------------------|
                                                        \         2         /                               \         2         /
---------------------------------------------------------------------------------------------------------------------------------
                                   _________________        _________________                                                    
                                  /   2        2         4 /   2        2        /atan2(im(x), re(x))\                           
                            4 + \/  im (x) + re (x)  - 4*\/  im (x) + re (x) *cos|-------------------|                           
                                                                                 \         2         /
$$\frac{4 i \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 8 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 3 \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - 4}{- 4 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + 4}$$ 
(-4 - 3*sqrt(im(x)^2 + re(x)^2) + 8*(im(x)^2 + re(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) + 4*i*(im(x)^2 + re(x)^2)^(1/4)*sin(atan2(im(x), re(x))/2))/(4 + sqrt(im(x)^2 + re(x)^2) - 4*(im(x)^2 + re(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2))
    © Sr Examen – Калькулятор