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Math Help - Complex Analysis Question

  1. #1
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    Cool Complex Analysis Question

    I'm having trouble with this showing question.


    Any help would be much appreciated. thanks!
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  2. #2
    MHF Contributor chisigma's Avatar
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    Setting z= x + i\cdot  y and f(z)= u(x,y) + i\cdot  v(x,y), f(*) is analytic in a region A of the complex plane if and only if in that region is...

    \frac{\partial u}{\partial x}=\frac{\partial v}{\partial y}

    \frac{\partial u}{\partial y}=- \frac{\partial v}{\partial x} (1)

    But f(*) is a real function in A so that is v(z)=0 and therefore for the (1) is \frac{\partial u}{\partial x} = \frac{\partial u}{\partial y}=0...

    Kind regards

    \chi \sigma
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  3. #3
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    how did you arise to f(*) is a real function in A so that v(z) = 0 ?

    thanks for the reply!
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