Beurling transform

Question

I wounder what is the value of the following integral $$\displaystyle A(z) = \lim_{\delta \to 0}\int_{|w|<1, |w-z|\ge \delta} \frac{|w|^ndu dv}{w^n(w-z)^2 },$$ where $n$ is an integer and $|z|<1$ and $w=u+iv$.