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.
a bijective conformal map from the unit disk to the upper half plane is given by
z | --> i (1 + z)/(1 - z),
(a Mobius ...
This shows how to find a bijective conformal mapping from a bounded region to an unbounded, and complete a proof regarding a conformal map.