Theorem 10.2.  Let f(z) be analytic at the point [Graphics:Images/ConformalMappingMod_gr_111.gif].  If [Graphics:Images/ConformalMappingMod_gr_112.gif] [Graphics:Images/ConformalMappingMod_gr_113.gif]and  [Graphics:Images/ConformalMappingMod_gr_114.gif],  then the mapping [Graphics:Images/ConformalMappingMod_gr_115.gif] magnifies angles at the vertex [Graphics:Images/ConformalMappingMod_gr_116.gif] by the factor k, as shown in Figure 10.3.

Figure 10.3  The analytic mapping [Graphics:Images/ConformalMappingMod_gr_117.gif] at point [Graphics:Images/ConformalMappingMod_gr_118.gif], where [Graphics:Images/ConformalMappingMod_gr_119.gif] [Graphics:Images/ConformalMappingMod_gr_120.gif]and  [Graphics:Images/ConformalMappingMod_gr_121.gif].

Proof.

Proof of Theorem 10.2 is in the book.

 

Complex Analysis for Mathematics and Engineering