(a)[5]
Find the solutions of $(1 + 2i)w^2 + 4w - (1 - 2i) = 0$, and give each answer in the form $x + iy$, where $x$ and $y$ are real.
(b)[5]
On a sketch of an Argand diagram, shade the set of points representing complex numbers that satisfy the inequalities $|z - 1 - i| \leq 2$ and $-\frac{1}{4}\pi < \arg z \leq \frac{1}{4}\pi$.