Find roots of polynomial $$ p(x) = x^{20}+1 $$

The roots of polynomial $ p(x) $ are:

$$ \begin{aligned}x_1 &= 0.7071+0.7071i\\[1 em]x_2 &= 0.7071-0.7071i\\[1 em]x_3 &= -0.454+0.891i\\[1 em]x_4 &= -0.454-0.891i\\[1 em]x_5 &= -0.7071+0.7071i\\[1 em]x_6 &= -0.7071-0.7071i\\[1 em]x_7 &= 0.454+0.891i\\[1 em]x_8 &= 0.454-0.891i\\[1 em]x_9 &= -0.891+0.454i\\[1 em]x_{10} &= -0.891-0.454i\\[1 em]x_{11} &= -0.1564+0.9877i\\[1 em]x_{12} &= -0.1564-0.9877i\\[1 em]x_{13} &= 0.891+0.454i\\[1 em]x_{14} &= 0.891-0.454i\\[1 em]x_{15} &= 0.1564+0.9877i\\[1 em]x_{16} &= 0.1564-0.9877i\\[1 em]x_{17} &= -0.9877+0.1564i\\[1 em]x_{18} &= -0.9877-0.1564i\\[1 em]x_{19} &= 0.9877+0.1564i\\[1 em]x_{20} &= 0.9877-0.1564i \end{aligned} $$

Polynomial $ x^{20}+1 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.

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