(a)[6]
The complex numbers $z$ and $w$ are defined by $z + (1 + i)w = i$ and $(1 - i)z + iw = 1$. Solve these equations for $z$ and $w$, and give each answer in the form $x + iy$, where $x$ and $y$ are real.
(b)[4]
The complex numbers $u$ and $v$ are given by $u = 1 + (2\sqrt{3})i$ and $v = 3 + 2i$. On an Argand diagram, the points $A$ and $B$ represent $u$ and $v$. A third point $C$ lies in the first quadrant, with $BC = 2AB$ and angle $ABC = 90^\circ$. Find the complex number $z$ represented by $C$, giving your answer exactly in the form $x + iy$, where $x$ and $y$ are real and exact.