Problem

1. $z_1 = 3 + 3i$, $z_2 = p + qi$, $p, q \in \mathbb{R}$

Given that $|z_1 z_2| = 15\sqrt{2}$

(a) determine $|z_2|$

Given also that $p = -4$

(b) determine the possible values of $q$

(c) Show $z_1$ and the possible positions for $z_2$ on the same Argand diagram.