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.

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, ...

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 ...

In this video series, I will show you how to divide complex numbers. We do this by eliminating the imaginary number in the denominator by producing equivalent fractions. We do this by multiplying by \ ...

All non-trivial zeros of the zeta function have real part one-half. Unfortunately, all those negative even numbers are trivial zeros. So … where are these non-trivial ones? To answer that, I must take ...

If you have ever read advanced textbooks or papers about electronics, you may have been surprised to see the use of complex numbers used in the analysis of AC circuits. A complex number has two parts: ...

Imagine winding the hour hand of a clock back from 3 o’clock to noon. Mathematicians have long known how to describe this rotation as a simple multiplication: A number representing the initial ...

Physicists construct theories to describe nature. Let us explain it through an analogy with something that we can do in our everyday life, like going on a hike in the mountains. To avoid getting lost, ...

Physicists from Heinrich Heine University Düsseldorf (HHU) have examined a fundamental property of quantum mechanics in collaboration with the German Aerospace Center (DLR). In an article published in ...