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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Complex analysis question
Replies: 10   Last Post: Jan 2, 2013 2:47 PM

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J. Antonio Perez M.

Posts: 2,736
Registered: 12/13/04
Re: Complex analysis question
Posted: Jan 2, 2013 9:51 AM
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On Wednesday, January 2, 2013 2:19:02 PM UTC+2, ksoileau wrote:
> Does anyone know of an easy proof of the following:
>
>
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> 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.
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> 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)

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