The real locus of $P_\alpha$ is the curve $C_{m,\alpha}=\{z:\operatorname{Re}(z^m(|z|^2+\alpha))=0\}$

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The real locus of $P_\alpha$ is the curve $C_{m,\alpha}=\{z:\operatorname{Re}(z^m(|z|^2+\alpha))=0\}$ · Prove2Me