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Cx-5x^4 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
         4    
c*x - 5*x  = 0
cx−5x4=0c x - 5 x^{4} = 0
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
        _________________                                      _________________                              /          _________________                                          _________________                         \           _________________                                          _________________                              /          _________________                                          _________________                         \           _________________                                          _________________                         
 2/3 6 /   2        2        /atan2(im(c), re(c))\      2/3 6 /   2        2        /atan2(im(c), re(c))\     |   2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\|    2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\     |   2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\|    2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\
5   *\/  im (c) + re (c) *cos|-------------------|   I*5   *\/  im (c) + re (c) *sin|-------------------|     |  5   *\/  im (c) + re (c) *sin|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *cos|-------------------||   5   *\/  im (c) + re (c) *cos|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *sin|-------------------|     |  5   *\/  im (c) + re (c) *sin|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *cos|-------------------||   5   *\/  im (c) + re (c) *cos|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *sin|-------------------|
                             \         3         /                                  \         3         /     |                               \         3         /                                      \         3         /|                                \         3         /                                      \         3         /     |                               \         3         /                                      \         3         /|                                \         3         /                                      \         3         /
-------------------------------------------------- + ---------------------------------------------------- + I*|- -------------------------------------------------- - --------------------------------------------------------| - -------------------------------------------------- + -------------------------------------------------------- + I*|- -------------------------------------------------- + --------------------------------------------------------| - -------------------------------------------------- - --------------------------------------------------------
                        5                                                     5                               \                          10                                                      10                           /                           10                                                      10                                \                          10                                                      10                           /                           10                                                      10
((523i(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)5+523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)5)+(i(−523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10−3⋅523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10)+3⋅523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10−523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10))+(i(−523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10+3⋅523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10)−3⋅523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10−523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10)\left(\left(\frac{5^{\frac{2}{3}} i \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{5} + \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{5}\right) + \left(i \left(- \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} - \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10}\right) + \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} - \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10}\right)\right) + \left(i \left(- \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} + \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10}\right) - \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} - \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10}\right) 
=
  /          _________________                                          _________________                         \     /          _________________                                          _________________                         \             _________________                         
  |   2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\|     |   2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\|      2/3 6 /   2        2        /atan2(im(c), re(c))\
  |  5   *\/  im (c) + re (c) *sin|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *cos|-------------------||     |  5   *\/  im (c) + re (c) *sin|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *cos|-------------------||   I*5   *\/  im (c) + re (c) *sin|-------------------|
  |                               \         3         /                                      \         3         /|     |                               \         3         /                                      \         3         /|                                  \         3         /
I*|- -------------------------------------------------- - --------------------------------------------------------| + I*|- -------------------------------------------------- + --------------------------------------------------------| + ----------------------------------------------------
  \                          10                                                      10                           /     \                          10                                                      10                           /                            5
i(−523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10−3⋅523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10)+i(−523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10+3⋅523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10)+523i(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)5i \left(- \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} - \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10}\right) + i \left(- \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} + \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10}\right) + \frac{5^{\frac{2}{3}} i \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{5} 
producto
  /        _________________                                      _________________                         \ /  /          _________________                                          _________________                         \           _________________                                          _________________                         \ /  /          _________________                                          _________________                         \           _________________                                          _________________                         \
  | 2/3 6 /   2        2        /atan2(im(c), re(c))\      2/3 6 /   2        2        /atan2(im(c), re(c))\| |  |   2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\|    2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\| |  |   2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\|    2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\|
  |5   *\/  im (c) + re (c) *cos|-------------------|   I*5   *\/  im (c) + re (c) *sin|-------------------|| |  |  5   *\/  im (c) + re (c) *sin|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *cos|-------------------||   5   *\/  im (c) + re (c) *cos|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *sin|-------------------|| |  |  5   *\/  im (c) + re (c) *sin|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *cos|-------------------||   5   *\/  im (c) + re (c) *cos|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *sin|-------------------||
  |                             \         3         /                                  \         3         /| |  |                               \         3         /                                      \         3         /|                                \         3         /                                      \         3         /| |  |                               \         3         /                                      \         3         /|                                \         3         /                                      \         3         /|
0*|-------------------------------------------------- + ----------------------------------------------------|*|I*|- -------------------------------------------------- - --------------------------------------------------------| - -------------------------------------------------- + --------------------------------------------------------|*|I*|- -------------------------------------------------- + --------------------------------------------------------| - -------------------------------------------------- - --------------------------------------------------------|
  \                        5                                                     5                          / \  \                          10                                                      10                           /                           10                                                      10                           / \  \                          10                                                      10                           /                           10                                                      10                           /
0(523i(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)5+523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)5)(i(−523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10−3⋅523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10)+3⋅523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10−523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10)(i(−523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10+3⋅523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10)−3⋅523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10−523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10)0 \left(\frac{5^{\frac{2}{3}} i \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{5} + \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{5}\right) \left(i \left(- \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} - \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10}\right) + \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} - \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10}\right) \left(i \left(- \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} + \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10}\right) - \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} - \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10}\right) 
=
0
00 
0
Respuesta rápida [src] 
x1 = 0
x1=0x_{1} = 0 
             _________________                                      _________________                         
      2/3 6 /   2        2        /atan2(im(c), re(c))\      2/3 6 /   2        2        /atan2(im(c), re(c))\
     5   *\/  im (c) + re (c) *cos|-------------------|   I*5   *\/  im (c) + re (c) *sin|-------------------|
                                  \         3         /                                  \         3         /
x2 = -------------------------------------------------- + ----------------------------------------------------
                             5                                                     5
x2=523i(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)5+523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)5x_{2} = \frac{5^{\frac{2}{3}} i \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{5} + \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{5} 
       /          _________________                                          _________________                         \           _________________                                          _________________                         
       |   2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\|    2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\
       |  5   *\/  im (c) + re (c) *sin|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *cos|-------------------||   5   *\/  im (c) + re (c) *cos|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *sin|-------------------|
       |                               \         3         /                                      \         3         /|                                \         3         /                                      \         3         /
x3 = I*|- -------------------------------------------------- - --------------------------------------------------------| - -------------------------------------------------- + --------------------------------------------------------
       \                          10                                                      10                           /                           10                                                      10
x3=i(−523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10−3⋅523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10)+3⋅523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10−523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10x_{3} = i \left(- \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} - \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10}\right) + \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} - \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} 
       /          _________________                                          _________________                         \           _________________                                          _________________                         
       |   2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\|    2/3 6 /   2        2        /atan2(im(c), re(c))\     ___  2/3 6 /   2        2        /atan2(im(c), re(c))\
       |  5   *\/  im (c) + re (c) *sin|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *cos|-------------------||   5   *\/  im (c) + re (c) *cos|-------------------|   \/ 3 *5   *\/  im (c) + re (c) *sin|-------------------|
       |                               \         3         /                                      \         3         /|                                \         3         /                                      \         3         /
x4 = I*|- -------------------------------------------------- + --------------------------------------------------------| - -------------------------------------------------- - --------------------------------------------------------
       \                          10                                                      10                           /                           10                                                      10
x4=i(−523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10+3⋅523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10)−3⋅523(re⁡(c))2+(im⁡(c))26sin⁡(atan2⁡(im⁡(c),re⁡(c))3)10−523(re⁡(c))2+(im⁡(c))26cos⁡(atan2⁡(im⁡(c),re⁡(c))3)10x_{4} = i \left(- \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} + \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10}\right) - \frac{\sqrt{3} \cdot 5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} - \frac{5^{\frac{2}{3}} \sqrt[6]{\left(\operatorname{re}{\left(c\right)}\right)^{2} + \left(\operatorname{im}{\left(c\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(c\right)},\operatorname{re}{\left(c\right)} \right)}}{3} \right)}}{10} 
x4 = i*(-5^(2/3)*(re(c)^2 + im(c)^2)^(1/6)*sin(atan2(im(c, re(c))/3)/10 + sqrt(3)*5^(2/3)*(re(c)^2 + im(c)^2)^(1/6)*cos(atan2(im(c), re(c))/3)/10) - sqrt(3)*5^(2/3)*(re(c)^2 + im(c)^2)^(1/6)*sin(atan2(im(c), re(c))/3)/10 - 5^(2/3)*(re(c)^2 + im(c)^2)^(1/6)*cos(atan2(im(c), re(c))/3)/10)
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