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Complex number z^2020 geometric series

2175ExpertPolynomialsComplex Numbers

Olimpiada Republicană la Matematică

Let $z$ be a complex number such that $z^{2020}|z|+\bar{z} i=0$. Determine the set of values of the expression $$ E=z^{2020}-z^{2019} i+\cdots+(-1)^{k} z^{2020-k} i^{k}+\cdots+z i+1 $$
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