A few hints:

- If \(z_1, z_2\) are complex roots to a quadratic equation, how are they related?

- Can you express the points \(P_1, P_2\) in terms of \(a, b, c\)?

- If possible, graph the origin and these two points on the Argand plane (does require you get the first hint) - what do you notice about the position of these points?

- Connect each point to the origin so you have segments \(OP_1\) and \(OP_2\). Is there a relationship between these segments and the angles they make with the coordinate axes?

- You can use the fact that \(\cos (\angle P_1OP_2) = \frac{P_1 \ \bullet \ P_2}{|P_1||P_2|}\) - but is there an easier method? (Think geometrically rather than algebraically)

Hope this helps