5 The cubic equation $$z ^ { 3 } + p z ^ { 2 } + q z + 37 - 36 \mathrm { i } = 0$$ where \(p\) and \(q\) are constants, has three complex roots, \(\alpha , \beta\) and \(\gamma\). It is given that \(\beta = - 2 + 3 \mathrm { i }\) and \(\gamma = 1 + 2 \mathrm { i }\).

1. 1. Write down the value of \(\alpha \beta \gamma\).
   2. Hence show that \(( 8 + \mathrm { i } ) \alpha = 37 - 36 \mathrm { i }\).
   3. Hence find \(\alpha\), giving your answer in the form \(m + n \mathrm { i }\), where \(m\) and \(n\) are integers.
2. Find the value of \(p\).
3. Find the value of the complex number \(q\).