8.
$$\mathrm { f } ( z ) = z ^ { 4 } + 6 z ^ { 3 } + 76 z ^ { 2 } + a z + b$$
where \(a\) and \(b\) are real constants.
Given that \(- 3 + 8 \mathrm { i }\) is a complex root of the equation \(\mathrm { f } ( z ) = 0\)
- write down another complex root of this equation.
- Hence, or otherwise, find the other roots of the equation \(\mathrm { f } ( z ) = 0\)
- Show on a single Argand diagram all four roots of the equation \(\mathrm { f } ( z ) = 0\)
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