# conformal map, unit disk

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• March 6th 2010, 12:35 PM
xboxlive89128
conformal map, unit disk
Let $\phi(z)$ be a conformal map from a domain D onto the open unit disk $\mathbb{D}$. For $0, let $D_r$ be the set of $z \in D$ such that $|\phi(z)|. Find a conformal map of $D_r$ onto $\mathbb{D}$.

The back of the book said that $\phi_r(z)=\frac{z}{r}$ works. I see how this map works. However, I don't see how to prove that this map is conformal. Thanks.
• March 6th 2010, 01:33 PM
Bruno J.
Being an analytic, univalent map it is certainly conformal!