(a) Without using a calculator, solve the equation

\(3w + 2iw^* = 17 + 8i\),

where \(w^*\) denotes the complex conjugate of \(w\). Give your answer in the form \(a + bi\).

(b) In an Argand diagram, the loci

\(\arg(z - 2i) = \frac{1}{6}\pi\) and \(|z - 3| = |z - 3i|\)

intersect at the point \(P\). Express the complex number represented by \(P\) in the form \(re^{i\theta}\), giving the exact value of \(\theta\) and the value of \(r\) correct to 3 significant figures.