** quiz-style questions:** 
    * Find expressions for $\sin(2\theta)$ and $\sin(3\theta)$ in terms of $\cos(\theta), \sin(\theta)$.
    * Compute $(\frac{1+i}{\sqrt{2}})^{20}$
    * Sketch the region $\vert z-1 \vert + \vert z + 1 \vert \leq 3$.