Any hint to compute the Green's function:

If $\Delta_z G(z,z') = 2\pi \delta^2(z-z')$, then

$$ G(z,z')=-2\pi \int \frac{d^2q}{4\pi^2}\frac{e^{iq(z-z')}}{q^2} = ln|\mu(z-z')| $$ where $\mu$ is some infrared cutoff at $q=0$.

I can see the first step is Fourier transform and inverse Fourier transform but I don't know how to figure out the second step. Thank you.