4. The complex number \(z\) is given by
$$z = \frac { p + 2 \mathrm { i } } { 3 + p \mathrm { i } }$$
where \(p\) is an integer.
- Express \(z\) 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 \(\arg ( z ) = \theta\), where \(\tan \theta = 1\) find the possible values of \(p\).