- \(\mathrm { f } ( \mathrm { z } ) = \mathrm { z } ^ { 3 } + a \mathrm { z } ^ { 2 } + b \mathrm { z } + 175 \quad\) where \(a\) and \(b\) are real constants
Given that \(- 3 + 4 \mathrm { i }\) is a root of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
- 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.
- Write down the roots of the equation \(\mathrm { f } ( \mathrm { z } + 2 ) = 0\)