(a)[5]
Determine $u$ and $w$, with each answer written in the form $x + iy$, where $x$ and $y$ are exact real values.
(b)[5]
On a sketch of an Argand diagram, shade the set of points for complex numbers $z$ that satisfy $|z - 2 - 2i| \leq 2$, $0 \leq \arg z \leq \frac{1}{4}\pi$ and $\operatorname{Re} z \leq 3$.