7. $$f ( z ) = z ^ { 4 } - 6 z ^ { 3 } + p z ^ { 2 } + q z + r$$ where \(p , q\) and \(r\) are real constants.
The roots of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\) are \(\alpha , \beta , \gamma\) and \(\delta\) where \(\alpha = 3\) and \(\beta = 2 + \mathrm { i }\)
Given that \(\gamma\) is a complex root of \(\mathrm { f } ( \mathrm { z } ) = 0\)

1. 1. write down the root \(\gamma\),
   2. explain why \(\delta\) must be real.
2. Determine the value of \(\delta\).
3. Hence determine the values of \(p , q\) and \(r\).
4. Write down the roots of the equation \(\mathrm { f } ( - 2 \mathrm { z } ) = 0\)