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

1. ## 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.

2. 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.