Complex numbers are created when you add a real number and an imaginary number (like “i”). These numbers are used throughout ...

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, ...

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 ...

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 ...

Mathematicians were disturbed, centuries ago, to find that calculating the properties of certain curves demanded the seemingly impossible: numbers that, when multiplied by themselves, turn negative.

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 ...

Complex-valued neural networks represent an evolving frontier where the intrinsic properties of complex numbers—magnitude and phase—are harnessed to develop richer and more robust representations of ...

William Ross does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their ...