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# A Complex Numbers Problem

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Let $a$, $b$, and $c$ be complex numbers such that $|a|=|b|=|c|=1$ and $\frac{a^2}{bc}+\frac{b^2}{ac}+\frac{c^2}{ab}=-1$. Find all positive values of $|a+b+c|$.

Jan 12, 2021