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Math Help - conformal map, unit disk

  1. #1
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    conformal map, unit disk

    Let \phi(z) be a conformal map from a domain D onto the open unit disk \mathbb{D}. For 0<r<1, let D_r be the set of z \in D such that |\phi(z)|<r. 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.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Being an analytic, univalent map it is certainly conformal!
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