(i)[5]
Write $u$ in the form $re^{i\theta}$, where $r > 0$ and $-\pi < \theta \leq \pi$, and give the exact values of $r$ and $\theta$. Then, or by another method, state the exact modulus and argument of $u^4$.
(ii)[3]
Confirm that $u$ is a root of $z^3 - 8z + 8\sqrt{3} = 0$ and state the other complex root of this equation.
(iii)[5]
On a sketch of an Argand diagram, shade the set of points that represent complex numbers $z$ for which $|z - u| \leq 2$ and $\operatorname{Im}\, z \geq 2$, where $\operatorname{Im}\, z$ is the imaginary part of $z$.