**Theorem 10.2.** Let
f(z) be analytic at the point . If
and , then
the mapping
magnifies angles at the vertex
by the factor k, as shown in Figure 10.3.

** Figure
10.3** The analytic mapping
at point ,
where
and .

**Proof.**

**Proof of Theorem 10.2 is in the
book.**

__Complex
Analysis for Mathematics and Engineering__