**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__