Theorem 10.1 (Conformal Mapping).  Let f(z) be an analytic function in the domain D, and let [Graphics:Images/ConformalMappingMod_gr_48.gif] be a point in D.  If  [Graphics:Images/ConformalMappingMod_gr_49.gif],  then f(z) is conformal at [Graphics:Images/ConformalMappingMod_gr_50.gif].

Figure 10.2  The analytic mapping [Graphics:Images/ConformalMappingMod_gr_51.gif] is conformal at the point [Graphics:Images/ConformalMappingMod_gr_52.gif], where [Graphics:Images/ConformalMappingMod_gr_53.gif].

Proof.

Proof of Theorem 10.1 is in the book.

 

Complex Analysis for Mathematics and Engineering