4.
$$f ( z ) = 2 z ^ { 4 } - 19 z ^ { 3 } + A z ^ { 2 } + B z - 156$$
where \(A\) and \(B\) are constants.
The complex number \(5 - \mathrm { i }\) is a root of the equation \(\mathrm { f } ( \mathrm { z } ) = 0\)
- Write down another complex root of this equation.
- Solve the equation \(\mathrm { f } ( \mathrm { z } ) = 0\) completely.
- Determine the value of \(A\) and the value of \(B\).