# Mobius transformation satisfying certain properties I'm having some trouble showing that

Mobius transformation satisfying certain properties
I'm having some trouble showing that a Mobius transformation F maps 0 to to 0 iff $F\left(z\right)={dz}^{-1}$ for some $d\in \mathbb{C}$. Mainly with the "only if" part. Do I need to use pictures?
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patriette65s
Write $f\left(z\right)=\frac{az+b}{cz+d}$. What are f(0) and $f\left(\mathrm{\infty }\right)$ in terms of a,b,c,d? Deduce further.
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