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Math Help - how do u find the functions orthogonal to this

  1. #1
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    how do u find the functions orthogonal to this

     \phi(x,y)=e^{x}(x\cos y-y\sin y)=c , \ \ \ \ c \ \ \ constant \ \

    what is the family of curves orthogonal to this phi.
    Last edited by silversand; January 31st 2009 at 04:05 PM.
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  2. #2
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    Quote Originally Posted by silversand View Post
     \phi(x,y)=e^{x}(x\cos y-y\sin y)=c , \ \ \ \ c \ \ \ constant \ \

    what is the family of curves orthogonal to this phi.
    This looks like a question from complex variable theory. If z = x + iy then e^{x}(x\cos y-y\sin y) is the real part of the analytic function ze^z. For any analytic function f(z), the family of curves given by Im(f(z)) = const. will be orthogonal to the family of curves Re(f(z)) = const.
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