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

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ksoileau

Posts: 85
From: Houston, TX
Registered: 3/9/08
Re: Complex analysis question
Posted: Jan 2, 2013 10:02 AM
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On Wednesday, January 2, 2013 8:51:23 AM UTC-6, Toni...@yahoo.com wrote:
> On Wednesday, January 2, 2013 2:19:02 PM UTC+2, ksoileau wrote:
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> > 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!
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> > Kerry M. Soileau
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> Hints:
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> (1) Develop f as a power series around any point c on the interior of C
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> (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.



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