For 2.31, let $z=x+yi$, and write out the two requirements as inequalities about $x$ and $y$, and draw the diagram.

2.32: If you let the two sums be $C$ and $S$ respectively, then $C+iS$ can be written as $$\epsilon + 2\epsilon^2 + 3\epsilon^3 + \cdots + (n-1)\epsilon^{n-1}$$ where $\epsilon$ is the $n$th root of unity. You need to find a way to simplify this sum.

4.20: Use polar coordinates: $x=r\cos\theta$ and $y=r\sin\theta$. Then plug into the expression and apply the trig formulas.