This video has a wonderful visualization on what complex roots look like. It is the first in a series of videos on imaginary numbers.

This video has a wonderful visualization on what complex roots look like. It is the first in a series of videos on imaginary numbers.

I watched the entire sequence of 13 or so videos from Welch Labs on complex numbers & functions between them, and I checked Wolfram Mathworld for the definition of “hyperplane”. I think your title should just read “Quadratic roots in the complex plane”.