Complex roots of a quadratic

Quadratic roots (complex)

The dashed red parabola is the reflection of the parabola in its turning point. The intersection of this with the x-axis is marked on both the Cartesian and Argand diagram. The complex roots correspond to the complex numbers at the top and bottom of a circle through these points on an Argand diagram.

The Cartesian plane (left) and Argand diagram (right)