(a(i))[2]
The complex number $u$ is given by $u = \frac{5}{a + 2i}$, where $a$ is a real constant. Write $u$ in the form $x + iy$, with $x$ and $y$ both real.
(a(ii))[3]
Determine the value of $a$ such that $\arg(u^*) = \frac{3}{4}\pi$, where $u^*$ is the complex conjugate of $u$.
(b)[4]
On a sketch of an Argand diagram, shade the area containing the complex numbers $z$ that satisfy both $|z| < 2$ and $|z| < |z - 2 - 2i|$.