(a)[5]
The complex numbers $u$ and $v$ are defined by the equations $u + 2v = 2i$ and $iu + v = 3$. Solve these equations for $u$ and $v$, and present both answers in the form $x + iy$, where $x$ and $y$ are real.
(b)[5]
On an Argand diagram, sketch the locus of complex numbers $z$ satisfying $|z + i| = 1$ and the locus of complex numbers $w$ satisfying $\arg(w - 2) = \frac{3\pi}{4}$. Find the least possible value of $|z - w|$ for points on these loci.