For this question, a calculator must not be used. The complex numbers $-3\sqrt{3} + i$ and $\sqrt{3} + 2i$ are called $u$ and $v$ respectively.
(i)[5]
Find the complex numbers $uv$ and $\frac{u}{v}$ in the form $x + iy$, where $x$ and $y$ are real and exact.
(ii)[3]
On a sketch of an Argand diagram with origin $O$, indicate the points $A$ and $B$ for the complex numbers $u$ and $v$ respectively. Show that angle $AOB = \frac{2}{3}\pi$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Insert $u$ and $v$ into $uv$, expand, and use $i^2=-1$” …