(i)[4]
Showing all your working, find, in the form $x + iy$, with $x$ and $y$ real, the complex numbers $u - 2w$ and $\frac{u}{w}$.
(ii)[2]
On an Argand diagram with origin $O$, the points $A$, $B$ and $C$ stand for the complex numbers $u$, $w$ and $u - 2w$ respectively. Prove that angle $AOB = \frac{1}{4}\pi$.
(iii)[2]
State the full geometrical relationship between the line segments $OB$ and $CA$.