how do u find the functions orthogonal to this

**silversand** · January 31st 2009, 02:40 PM

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

what is the family of curves orthogonal to this phi.

**Opalg** · February 1st 2009, 12:20 AM

Originally Posted by silversand

$\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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