Question
$$i^{29}+i^{21}+i = 0$$
Answer
$$ i = 0 $$
Explanation
In order to solve $ \color{blue}{ x^{29}+x^{21}+x = 0 } $, first we need to factor our $ x $.
$$ x^{29}+x^{21}+x = x \left( x^{28}+x^{20}+1 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The remaining roots can be found by solving equation $ x^{28}+x^{20}+1 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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