ksoileau
Posts:
83
From:
Houston, TX
Registered:
3/9/08


Re: Complex analysis question
Posted:
Jan 2, 2013 10:02 AM


On Wednesday, January 2, 2013 8:51:23 AM UTC6, Toni...@yahoo.com wrote: > 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)
I don't mean to be dense, but it's not clear from the hypothesis that f'(z)=0, only that the derivative of f(z) along C is zero.

