Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them. Problems in ...

In this math tutorial I will show you how to multiply complex numbers. Complex numbers come in the form of a +bi. Multiplying complex numbers carry some of the same properties as multiplying ...

§RU.1 IN MY PRIMER ON THE SOLUTION of the general cubic, I mentioned the cube roots of 1 (§CQ.4). There are three of these little devils. Obviously 1 itself is a cube root of 1, since 1×1×1 = 1. The ...

Imaginary numbers might seem like unicorns and goblins — interesting but irrelevant to reality. But for describing matter at its roots, imaginary numbers turn out to be essential. They seem to be ...