If $z\mapsto az+b$ with $a\ne0$ sends $C_{m,\alpha}$ into itself, then $b=0$ and $a^{2m}=1$

Initializing...

If $z\mapsto az+b$ with $a\ne0$ sends $C_{m,\alpha}$ into itself, then $b=0$ and $a^{2m}=1$ · Prove2Me