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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.

##### 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.

##### Solution Preview

(a)

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

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

(a Mobius ...

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