(a)[3]
The complex number $\frac{3 - 5i}{1 + 4i}$ is labelled $u$. Show your working and express $u$ in the form $x + iy$, where $x$ and $y$ are real.
(b(i))[4]
On a sketch of an Argand diagram, shade the set of points representing complex numbers that satisfy the inequalities $|z - 2 - i| \leq 1$ and $|z - i| \leq |z - 2|$.
(b(ii))[2]
Calculate the maximum value of $\arg z$ for points in the shaded region.