Show all working, and write the complex number $\frac{2 + 3i}{1 - 2i}$ in the form $r e^{i\theta}$, with $r > 0$ and $-\pi < \theta \leq \pi$. State $r$ and $\theta$ correct to 3 significant figures.
(b)[4]
On an Argand diagram, sketch the locus of complex numbers $z$ that satisfy $|z - 3 + 2i| = 1$. Determine the least value of $|z|$ for points on this locus, and give your answer exactly.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Either multiply the numerator and denominator by $1+2i$, or use an equivalent method, or set the expression equal to $x+iy$ and solve” …