Harmonic Functions and Integrating Along Curves: The Role of 90 Degree Rotations

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If f is a smooth function defined on the plane then the integral of its gradient over any closed curve is zero.

What about the integral of the 90 degree rotation of the gradient?

In symbols, if grad f = (df/dx , df/dy) its 90 degree rotation is

(-df/dy , df/dx)
 
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oops I got the answer. The function has to be harmonic.
 

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