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 ...

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 ...

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 ...

Have you ever sat in a math classroom and wondered, “When will I ever use this?” You might have asked yourself this question when you first encountered “imaginary” numbers, and with good reason: What ...

Our February Insights puzzle sent readers on a treasure hunt based on complex numbers. First we provided a bit of a primer, demonstrating that complex numbers (expressions of the form a + bi, where ...

In a previous post, I argued that concepts and concerns, such as free will and determinism, can be complex in the same sense in which numbers can be: in other words, in combining a real with an ...