(a)[2]
Determine the modulus and argument of $z$.
(b(i))
Express $z + 2z^*$ in the form $x + iy$, with $x$ and $y$ real and exact.
(b(ii))[4]
Write $\dfrac{z^*}{iz}$ in the form $x + iy$, where $x$ and $y$ are real and exact.
(c)[3]
On a sketch of an Argand diagram with origin $O$, place the points $A$ and $B$ to represent the complex numbers $z^*$ and $iz$ respectively. Prove that angle $AOB$ is equal to $\dfrac{pi}{6}$.