(a)[4]
Without a calculator, solve $3w + 2i w^* = 17 + 8i$, where $w^*$ is the complex conjugate of $w$. Give your answer in the form $a + bi$.
(b)[5]
On an Argand diagram, the loci $\arg(z - 2i) = \frac{1}{6}\pi$ and $|z - 3| = |z - 3i|$ meet at the point $P$. Write the complex number for $P$ in the form $re^{i\theta}$, giving the exact value of $\theta$ and $r$ correct to 3 significant figures.