For this question, calculator use is not allowed. The complex number $u$ is defined by $u = \frac{4i}{1 - (\sqrt{3})i}$.
(i)[3]
Express $u$ in the form $x + iy$, with $x$ and $y$ both real and exact.
(ii)[2]
Find the exact modulus and argument of $u$.
(iii)[4]
On a sketch of an Argand diagram, shade the region whose points represent complex numbers $z$ that satisfy the inequalities $|z| < 2$ and $|z - u| < |z|$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Multiply the numerator and denominator by $1+\sqrt3 i$, or any equivalent factor” …