(a)[5]
Show all working needed, and write the complex number $\frac{2 + 3i}{1 - 2i}$ in the form $re^{i\theta}$, where $r > 0$ 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 possible value of $|z|$ for points on this locus, and express your answer exactly.