(a)[3]
Find $\frac{u}{v}$ written in the form $x + iy$, where $x$ and $y$ are real.
(b)[2]
Hence write $\frac{u}{v}$ in the form $r e^{i\theta}$, with $r$ and $\theta$ exact.
(c)[2]
On an Argand diagram with origin $O$, points $A$, $B$ and $C$ correspond to the complex numbers $u$, $v$ and $2u + v$ respectively. State the full geometrical relationship between $OA$ and $BC$.
(d)[2]
Prove that the angle $AOB$ is $\frac{3}{4}\pi$.