From your knowledge of the map z to z^2, explain how the map z to e^z works. Discuss how to construct an inverse map. Make the domains and ranges clear in your discussion and use simple diagrams to clarify your answer.
Consider the wedge 0<=|z|<=r, and 0<=arg(z)<=(pie/4) in the z-plane. Find a 1-1 map that takes any point inside (but not on the boundary of) this wedge to a point inside (but not on the boundary of) the infinite horizontal strip in another copy of the z-plane that lies between the horizontal lines y=0 and y=2pie.
Help!!! For the second question, I am not sure how to parameterise....HELP!