(a(i))[3]
Express $u$ in Cartesian form $x + iy$, with $x$ and $y$ written in terms of $a$.
(a(ii))[3]
Find the exact value of $a$ when $\arg u = \dfrac{\pi}{3}$.
(b(i))[4]
On an Argand-diagram sketch, shade the set of points that correspond to complex numbers $z$ satisfying $|z - 2i| \leq |z - 1 - i|$ and $|z - 2 - i| \leq 2$.
(b(ii))[2]
Calculate the least value of $\arg z$ for the points in this region.