Theorem 10.1 (Conformal Mapping).  Let f(z) be an analytic function in the domain D, and let be a point in D.  If  ,  then f(z) is conformal at .

Figure 10.2  The analytic mapping is conformal at the point , where .

Proof.

Proof of Theorem 10.1 is in the book.

Complex Analysis for Mathematics and Engineering