@futurebird EE student here. The need for complex numbers is to encode the phase angle of the voltage. The absolute value equals the reactance (i.e. the value) and the phase angle shows the "offset" caused by the reactance. This is relevant for amplifiers for instance. As to why we use imaginary numbers, no idea.
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@fuchsi @llewelly @codefolio @jeffc @futurebird no idea. You can simulate complex circuits with multiple Ls and Cs in parallel and /or series and the total impedance just "adds" up. Stuff gets funky at high frequencies when even resistors start exhibiting a capacitive / inductive behavior.