(a)[3]
Write $u$ in terms of $a$ in the form $x + iy$, with $x$ and $y$ real and exact.
(b)[2]
It is now given that $a = 3$. Write $u$ in the form $re^{i\theta}$, where $r > 0$ and $-\pi < \theta \leq \pi$, and give the exact values of $r$ and $\theta$.
(c)[3]
Using your answer to part (b), determine the two square roots of $u$. Give them in the form $re^{i\theta}$, where $r > 0$ and $-\pi < \theta \leq \pi$, with exact values for $r$ and $\theta$.