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