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Math Help - Complex Numbers

  1. #1
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    Complex Numbers

    have tried to do this without much success.

    Find imaginary party v=v(x,y) such that
    f(z)=u+i*v
    for a u(x,y)=e(x)cos(y)

    I have tried something using the cartesian form of the cauchy riemann equations. and ended up getting . exp(x)*sin(y)+K, but i think im totally of.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by sebko View Post
    I have tried something using the cartesian form of the cauchy riemann equations. and ended up getting . exp(x)*sin(y)+K, but i think im totally of.

    That is right, u=e^x\cos y is harmonic on \mathbb{R}^2 so, there exists v such that f=u+iv is holomorphic in \mathbb{C} . Using the Cauchy Riemann equations we obtain v=e^x\sin y+k\;(k\in\mathbb{R}) . Then, f(z)=e^z+ki .
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  3. #3
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    Muchas Gracias!
    You have made it very clear
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