1.
$$\mathrm { f } ( \mathrm { z } ) = \mathrm { z } ^ { 3 } + a \mathrm { z } + 52 \quad \text { where } a \text { is a real constant }$$
Given that \(2 - 3 \mathrm { i }\) is a root of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
- write down the other complex root.
- Hence
- solve completely \(\mathrm { f } ( \mathrm { z } ) = 0\)
- determine the value of \(a\)
- Show all the roots of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\) on a single Argand diagram.