(i)[2]
Find the modulus and argument for $z.$
(ii(a))[4]
The complex conjugate of $z$ is written as $z^*$. With working shown, give $2z + z^*$ in the form $x + iy$, where $x$ and $y$ are real.
(ii(b))[4]
The complex conjugate of $z$ is written as $z^*$. With working shown, give $\frac{iz^*}{z}$ in the form $x + iy$, where $x$ and $y$ are real.
(iii)[3]
On a sketch of an Argand diagram with origin $O$, mark the points $A$ and $B$ to represent the complex numbers $z$ and $iz^*$ respectively. Show that angle $AOB = \frac{1}{6}\pi.$