# Prove ff is unique

Let AA be a simply connected region in C\mathbb{C}

Let Δ={z:|z|<1}\Delta=\{z : |z|\lt 1 \} Prove that if ff is a conformal and bijective map, so that it sends a point z0∈Az_0 \in A to the origin and f′(z0)>0f'(z_0 )\gt 0 , then ff is unique.

Any hints on how to prove this? I’m new to complex analyisis (using Marsden’s Book) and I’m a bit lost.

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