Complex roots of a cubic

Cubic roots (complex)

All cubics have at least one real root. If there is only one real roots, there will be a quadratic factor. The dashed red parabola represents the equation of this quadratic reflected in it's 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. (see also complex roots of a quadratic)

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