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    Conformal mapping

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    A) find a bijective conformal mapping that takes a bounded region to an unbounded region
    b) prove that a conformal map cannot take a simply connected region onto a region that is not simply connected.

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    a bijective conformal map from the unit disk to the upper half plane is given by

    z | --> i (1 + z)/(1 - z),

    (a Mobius ...

    Solution Summary

    This shows how to find a bijective conformal mapping from a bounded region to an unbounded, and complete a proof regarding a conformal map.