To show that if all roots (complex) of an integer polynomial have norm 1, then they are roots of 1 – math.stackexchange.com

To show that if all roots (complex) of an integer polynomial have norm 1, then they are roots of 1 – math.stackexchange.com

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We have, $f(x)=x^n + a_{n-1}x^{n-1} + \cdots + a_0 \in \mathbb{Z}[x]$, with $\alpha_i\in\mathbb{C},\ 1\leq i\leq n$ being all the roots of $f(x)$. If we have $|\alpha_i|=1$, for every $i$, then $\...

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