
Re: Complex analysis question
Posted:
Jan 2, 2013 9:51 AM


On Wednesday, January 2, 2013 2:19:02 PM UTC+2, ksoileau wrote: > Does anyone know of an easy proof of the following: > > > > If f is analytic inside and on a contour C, and f has constant modulus inside and on C, then f is constant inside and on C. > > > > Thanks for any replies! > > Kerry M. Soileau
Hints:
(1) Develop f as a power series around any point c on the interior of C
(2) Find the coefficient of (1) using Cauchy's Integral Theorem and Cauchy's Evaluation Theorem and use that f'(z)=0 (why)

