3 The cubic equation
$$z ^ { 3 } + 2 ( 1 - \mathrm { i } ) z ^ { 2 } + 32 ( 1 + \mathrm { i } ) = 0$$
has roots \(\alpha , \beta\) and \(\gamma\).
- It is given that \(\alpha\) is of the form \(k \mathrm { i }\), where \(k\) is real. By substituting \(z = k \mathrm { i }\) into the equation, show that \(k = 4\).
- Given that \(\beta = - 4\), find the value of \(\gamma\).