What uses do complex numbers have in physics?

Can anyone give me examples to fields or methods in physics that require the use of complex numbers?What uses do complex numbers have in physics?
AC theory uses complex numbers to denote phase differences and reactances.





http://www.opamp-electronics.com/tutoria鈥?/a>What uses do complex numbers have in physics?
Complex numbers are not absolutely required to solve any problem in physics, but the mathematics involved with problems that involve linear differential equations is made much simpler. The reason for this is that De^(ix)=iDe^(ix), where D is derivative wrt x. That is, differentiation is reduced to multiplication by a constant. This turns linear differential equations into much more tractible polynomials.





The real component of e^(ix) is just .5*cos(x), and ultimately you only need the real component to represent a physical property. So technically, you can do everything with trig functions. But the math is much messier.
Some problems in electricity and quantum physics require the use of complex numbers in their solutions. As of right now, these are the only Physics topics that I can think of that requires complex numbers applications.
quantum mechanics requires the use of complex numbers for its maths.





wave functions in quantum mechanics, and traveling waves in general need complex numbers to describe propagation.