4.
$$f ( z ) = 2 z ^ { 3 } - z ^ { 2 } + a z + b$$
where \(a\) and \(b\) are integers.
The complex number \(- 1 - 3 \mathrm { i }\) is a root of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
- Write down another complex root of this equation.
- Determine the value of \(a\) and the value of \(b\).
- Show all the roots of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\) on a single Argand diagram.
| VIIN SIHILNI III IM ION OC | VIAV SIHI NI III HM ION OO | VIAV SIHI NI III IM I ON OC |