Integrate: $\oint_c (x^2 + iy^2)ds$ How do I integrate the following with $|z| = 2$ and $s$ is the arc length? The answer is $8\pi(1+i)$ but I can't seem to get it. $$\oint_c (x^2 + iy^2)ds$$

Use polars such that, for $\theta \in [0,2 \pi)$:

$$x = 2 \cos{\theta}$$ $$y = 2 \sin{\theta}$$

$$ds = 2 d\theta$$

That last relation is from the length of an arc of a circle of radius $r$, that is, $ds = r d\theta$.