Real and imaginary: The time-dependent Schrödinger equation formulated using complex numbers. (Courtesy: iStock/piranka) Complex numbers are essential to achieve the most accurate quantum-mechanical ...

Areas of pure math such as algebra, analysis, combinatorics and many others can be used—in some cases combined—to solve the complex math problems arising from applications of math to the real world.

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, ...

This course will introduce you to the theory of functions of complex variables, which is a core area of mathematics. It is a basic tool in many mathematical theories. We will cover complex numbers and ...

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, ...

An illustration of physics equations being bent and warped. New research has found a way to accurately predict quantum interactions without using complex numbers. | Credit: vitacopS via Getty Images ...

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 ...

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, ...