(a)[3]
You are given $z_1 = r_1 e^{i\theta_1}$ and $z_2 = r_2 e^{i\theta_2}$. Show that $(z_1 z_2)^* = z_1^* z_2^*$.
(b)[3]
$z = 3e^{i\frac{\pi}{4}}$ is a root of the equation $z^2 + bz + c = 0$, with $b$ and $c$ real. State the other root and hence determine $b$ and $c$.