Question:
Using Green's Theorem, show that for a region in the complex plane $D$, with $z_0$ not in $D$, $$\iint_D \frac{1}{z_0-z} \,dx\,dy = \oint_{\partial D} \log(z_0-z)\,dy.$$
First of all, I'm pretty sure the $dy$ is a typo on the right hand side, and should read "$dz$". In any event, I'm totally lost on how to do this. I know that I can write $\log(z_0-z)$ as $\log|z_0-z| + i\arg(z_0-z)$, but this doesn't help me use Green's Theorem, since we can't take any partial derivatives of the $\arg$ function.
I know that Green's Theorem is $$\iint_D (Q_x - P_y) \,dx\,dy = \oint_{\partial D} P\,dx+Q\,dy,$$ but I'm having trouble making my equality look like this one.