(a)[3]
Express $u$ in the form $x + iy$, where $x$ and $y$ are real.
(b)[2]
Show the points $A$, $B$ and $C$ on a sketch of an Argand diagram to represent $u$, $7 + i$ and $1 - i$ respectively.
(c)[3]
Using the arguments of $7 + i$ and $1 - i$, show that $\tan^{-1}\left(\frac{4}{3}\right) = \tan^{-1}\left(\frac{1}{7}\right) + \frac{1}{4}\pi$.