(a)[3]
On an Argand diagram with origin $O$, indicate $A$, $B$ and $C$ for the complex numbers $u$, $u^{*}$ and $u^{*} - u$ respectively. State what kind of quadrilateral is formed by $O$, $A$, $B$ and $C$.
(b)[3]
Write $\frac{u^{*}}{u}$ in the form $x + iy$, with $x$ and $y$ real.
(c)[2]
Using the argument of $\frac{u^{*}}{u}$, or by any valid route, prove that $\tan^{-1}\!\left(\frac{3}{4}\right) = 2\tan^{-1}\!\left(\frac{1}{3}\right)$.