ksoileau
Posts:
74
From:
Houston, TX
Registered:
3/9/08
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Re: Complex analysis question
Posted:
Jan 2, 2013 10:07 AM
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On Wednesday, January 2, 2013 9:02:59 AM UTC-6, ksoileau wrote:
> On Wednesday, January 2, 2013 8:51:23 AM UTC-6, Toni...@yahoo.com wrote:
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> > 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)
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> 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.
f(z) might be of the form Kexp(ig(z)) for some mapping g of C into the reals, with K a nonnegative real number.
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