(a)[2]
Write $u$ in the form $re^{i\theta}$, where $r > 0$ and $-\pi < \theta \leq \pi$, and give the exact values of $r$ and $\theta$.
(b)[2]
Hence establish that $u^6$ is real and state its value.
(c(i))[4]
On an Argand diagram sketch, shade the region made up of points for complex numbers $z$ satisfying $0 \leq \arg(z - u) \leq \frac{\pi}{4}$ and $\Re z \leq 2$.
(c(ii))[2]
Determine the greatest value of $|z|$ for points in the shaded region, and give your answer correct to 3 significant figures.