Problem

4. $f(z) = 2z^3 - z^2 + az + b$

where $a$ and $b$ are integers.

The complex number $-1 - 3i$ is a root of the equation $f(z) = 0$

(a) Write down another complex root of this equation.

(b) Determine the value of $a$ and the value of $b$.

(c) Show all the roots of the equation $f(z) = 0$ on a single Argand diagram.