(a)[5]
Find the complex number $z$ that satisfies the equation $z + \frac{iz}{z^*} - 2 = 0$, with $z^*$ as the complex conjugate of $z$. Express your answer in the form $x + iy$, where $x$ and $y$ are real.
(b(i))[2]
On one Argand diagram sketch the loci described by $|z - 2i| = 2$ and $\operatorname{Im} z = 3$, where $\operatorname{Im} z$ means the imaginary part of $z$.
(b(ii))[2]
In the first quadrant, the two loci meet at point $P$. Find the exact argument of the complex number shown by $P$.