Sum involving 23rd roots of unity

2300ExpertComplex NumbersAlgebra

HMMT

Let $z$ be a non-real complex number with $z^{23}=1$. Compute $$ \sum_{k=0}^{22} \frac{1}{1+z^{k}+z^{2 k}} $$

0 students attempted0% solvedRating 2300

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2300ExpertComplex NumbersAlgebra

HMMT

Let $z$ be a non-real complex number with $z^{23}=1$. Compute $$ \sum_{k=0}^{22} \frac{1}{1+z^{k}+z^{2 k}} $$

0 students attempted0% solvedRating 2300