So I’m looking for some applications that are relatively easy to understand, ideally in like CS or physics, but anything works. I’ve seen it be talked about in discussions of oscillations (I have a pretty good basic understanding of pendulum motion, for example, but I don’t understand how complex numbers come in), or in AC currents (I have like 0 background in electricity and magnetism apart from basic high school physics with super basic DC systems), but I can never understand how we use complex numbers for that…
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A pendulum is an oscillation between kinetic and potential energy, it’s continuously converting one to another. An electromagnetic oscillation is similar, it converts energy between electrical and magnetic field. Because such things have two coupled but inherently different components it’s really convenient to represent them on a 2D number plane. Oscillation reduces to a vector rotation because the total energy in the system is constant represented by length of the vector, but shifting from one form to another represented by sine-cosine relation.
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