2. The complex numbers \(z _ { 1 } , z _ { 2 }\) and \(z _ { 3 }\) are given by
$$\mathrm { z } _ { 1 } = 2 - \mathrm { i } \quad \mathrm { z } _ { 2 } = p - \mathrm { i } \quad \mathrm { z } _ { 3 } = p + \mathrm { i }$$
where \(p\) is a real number.
- Find \(\frac { z _ { 2 } z _ { 3 } } { z _ { 1 } }\) in the form \(a + b \mathrm { i }\) where \(a\) and \(b\) are real. Give your answer in its simplest form in terms of \(p\).
Given that \(\left| \frac { z _ { 2 } z _ { 3 } } { z _ { 1 } } \right| = 2 \sqrt { 5 }\)
- find the possible values of \(p\).