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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Basically all control systems use complex numbers to develop their control laws.
When you write the differential equations for almost all real-world physical systems with controllers, complex numbers are going to show up in the solution if you’re using a Laplace transform, which is the most common way to do the analysis.
These are *everywhere*…your thermostat, your oven, your car, your phone, anything with an engine or motor, anything with a servo…they’re ubiquitous.
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