# Partial derivative of the harmonic complex function

For a harmonic function of a complex number ##z##, ##F(z)=\frac{1}{z}##, which can be put as ##F(z)=f(z)+g(\bar{z})##and satisfies ##\partial_xg=i\partial_yg##. But this function can also be put as ##F(z)=\frac{\bar{z}}{x^2+y^2}## which does not satisfy that derivative equation!

Sorry, I should have put this thread in homework section.

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Actually, if F is analytic, $\frac{\partial F}{\partial\bar{z}}=0$.