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

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)

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