1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

398 CHAPTER 10 • CONFORMAL MAPPINC

Therefore, the angle of rotation is given by

-7f

a1 = Argf' (i) =

2

,

az = Argj' (1) = 7f, and

0<3 = Argf' (7r + i) = ~'

respectively.

Let f be a nonconstant analytic function. If f' (z 0 ) = 0, then z 0 is called a

critical point off, and the mapping w = f (z) is not conformal at zo. Theorem

10.2 shows what happens at a critical point.