Let $\gamma$ be the circle in the complex plane given by $|z-i| = 1$, with counterclockwise orientation. Evaluate $$\int \frac{|z|^2}{(z-i)^2} dz$$
The function $|z|^2$ is not analytic. How would I set up the limits for this integral, is it just 0 to $2\pi$ because its a circle?