1.
$$z _ { 1 } = 3 + 3 i \quad z _ { 2 } = p + q i \quad p , q \in \mathbb { R }$$
Given that \(\left| z _ { 1 } z _ { 2 } \right| = 15 \sqrt { 2 }\)
- determine \(\left| z _ { 2 } \right|\)
Given also that \(p = - 4\)
- determine the possible values of \(q\)
- Show \(z _ { 1 }\) and the possible positions for \(z _ { 2 }\) on the same Argand diagram.