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Math Help - harmonic functions

  1. #1
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    harmonic functions

    How do I:

    Prove that if u and v are harmonic in a domain D, then (du/dy - dv/dx) + i(du/dx + dv/dy) is analytic in D.
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  2. #2
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    A complex function is analytic if it obeys the Cauchy-Riemann equations. Apply those to the complex function you want to prove is analytic, and use the fact that \frac{\partial^2u}{\partial{x}^2}+\frac{\partial^2  u}{\partial{y}^2}=0 and \frac{\partial^2v}{\partial{x}^2}+\frac{\partial^2  v}{\partial{y}^2}=0, as the functions are harmonic.

    --Kevin.
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