3.
$$f ( z ) = z ^ { 4 } + a z ^ { 3 } + b z ^ { 2 } + c z + d$$
where \(a , b , c\) and \(d\) are integers.
The complex numbers \(3 + \mathrm { i }\) and \(- 1 - 2 \mathrm { i }\) are roots of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
- Write down the other roots of this equation.
- Show all the roots of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\) on a single Argand diagram.
- Determine the values of \(a , b , c\) and \(d\).
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