Question: Let $z_1$ and $z_2$ be two roots of the equation $z^2 + az + b= 0$, where $z$ is complex. Further, assume the origin, $z_1$ and $z_2$ to form an equilateral triangle. Then, find the relation between $a$ and $b$.
I cannot think of a way to attempt this question. I tried drawing a diagram, but that didn't help. How should I begin the question?