Hello, I have a quick question that I imagine anyone who has studied physics or math at a university can answer rather easily. If not, I apologize in advance for the effort! What is the physical significance of imaginary numbers? I have heard repeatedly that imaginary numbers are relevant, that they do appear in the real world, and so on, but I haven't found a good example. I'm convinced that they're telling the truth, but I don't have anything to back that up. I found one page that tried to show how imaginary numbers could be used for calculating fast mental rotations, but it turned out they had just memorized points on a circle, just as you could with normal trigonometry. I have heard they are used in fluid dynamics, in electricity, in astrophysics, and any number of other settings, but I just haven't found an example. If someone can show me one, I can finally prove to the "math skeptics" that they're wrong! Cheers.