# A simple theorem on the zero’s of polynomials on the space of 3D complex numbers.

In this post we look in detail at a very simple yet important polynomial namely

p(X) = X (X – 1).

Why does it have four zero’s in the space of 3D complex numbers? Well if you solve for the zero’s of p so try to solve p(X) = 0, that is you are looking for all numbers such that X^2 = X.
These numbers are their own square, on the real line or on the complex plane there are only two numbers that are their own square namely 0 and 1.
On the space of 3D complex numbers we also have an exponential circle and the midpoint of that circle is the famous number alpha. It is a cakewalk to calculate that alpha is it’s own square just like (1 – alpha).

This post is four pictures long in the size 550×825 pixels so it is not such a long read this time. In case you are not familiar with this number alpha, use the search function on this website and search for the post “Seven properties of the number alpha”. Of course since it is math you will also need a few days time of thinking the stuff out, after all the human brain is not very good at mathematics…