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 ...

To a nonmathematician, having the letter "i" represent a number that does not quite exist and is "imaginary" can be hard to wrap your head around. If you open your mind to this way of thinking, ...

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 ...

A century ago, the strange behavior of atoms and elementary particles led physicists to formulate a new theory of nature. That theory, quantum mechanics, found immediate success, proving its worth ...

An international team of researchers shows through a concrete theoretical experiment that the prediction by standard complex quantum theory cannot be expressed by its real counterpart and ratifies its ...

Several years ago one of us, Toni, asked another of us, Marco, to come to his office at the Institute of Photonic Sciences, a large research center in Castelldefels near Barcelona. “There is a problem ...