No map $z\mapsto c/z$ pulls $P_{\bar\alpha}$ back to a multiple of $P_\alpha$ if $|\alpha|=1$, $\alpha\notin\mathbb R$

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No map $z\mapsto c/z$ pulls $P_{\bar\alpha}$ back to a multiple of $P_\alpha$ if $|\alpha|=1$, $\alpha\notin\mathbb R$ · Prove2Me