- The complex numbers \(z _ { 1 }\) and \(z _ { 2 }\) are given by
$$z _ { 1 } = p + 2 i \text { and } z _ { 2 } = 1 - 2 i$$
where \(p\) is an integer.
- Find \(\frac { z _ { 1 } } { z _ { 2 } }\) in the form \(a + b\) i where \(a\) and \(b\) are real. Give your answer in its simplest form in terms of \(p\).
Given that \(\left| \frac { z _ { 1 } } { z _ { 2 } } \right| = 13\),
- find the possible values of \(p\).