Let the function f (z) = u(x, y) + iv(x, y) be analytic in some domain D.

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Let the function f (z) = u(x, y) + iv(x, y) be analytic in some domain D. State why the functions
U(x, y) = eu(x,y) cos v(x, y), V (x, y) = eu(x,y) sin v(x, y)
are harmonic in D and why V (x, y) is, in fact, a harmonic conjugate of U(x, y).

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Complex Variables and Applications

ISBN: 978-0073051949

8th edition

Authors: James Brown, Ruel Churchill

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Question Posted: Jun 01, 2016 01:39 AM

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Let the function f (z) = u(x, y) + iv(x, y) be analytic in some domain D.

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If fz uz y ivx y is analytic in some domain D then Since e...View the full answer

Complex Variables and Applications

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