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