Show that the function w = e^z maps the shaded rectangle in Fig X one-to-one onto the semi-annulus in Fig y.
Fig x is the rectangle -1<x<1 ; 0<y<(x+pi(i))
Fig y is the semi-annulus such that y>0 and -e<r<-1/e
The Attempt at a Solution
I'm not quite sure how to show the function is one-to-one. Any tips would be much appreciated.