Question: Are complex numbers used in quantum physics equations? If so, why?

Arttu Rajantie answered on 18 Jun 2011:

Yes, quantum physics is most naturally described using complex numbers. It is intriguing because we do not seem to encounter them elsewhere in nature (although their use also simplifies calculations in electromagnetism). One can trace back the use of complex numbers to the symmetries of the theory, which in turn are connected to the fact that the number of particles is conserved.

There is a general pattern that when we move from the immediately observable things to more abstract theoretical concepts, we need to use more and more advanced maths. Primitive cultures used only positive integers and even the ancient Greeks thought that all numbers are rational. In particle physics we also need other types of numbers, such as Grassmann numbers for which a*b=-b*a.