Complex Quadratics

The normal quadratic you solve in school is Let's simplify and call it so it is centred around the axis and to make the visualisation easier. Now change to and replace the ordinary number with the complex number . Also replace with to give us . We know the complex number so substitute: Now ignoring the imaginary part we get This is plotted on the axis below along with two planes, and . Where these planes intercept the surface, we can see the standard 2D quadratic plots that you might be used to from school. As you move slider you can see that at no point is there no solution to the initial quadratic. (Thanks to bikinfo for the initial idea to create this visualisation)