Eli5: why do we incorporate imaginary numbers in various physics equations.
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Similar reason why we incorporate negative numbers.
Negative numbers are useful because they let us represent a thing having “two states.” Credit/debit, above/below sea level, towards/away, etc.
Complex numbers are used to represent cyclical things. If you multiply with -1, you end up flipping between the two directions (-1, +1, -1, +1…) but when you multiply with the imaginary unit i instead, you rotate between four directions (+1, i, -1, -i, +1…) which is very useful if we want to represent, say, the way a wave works. Quantum physics, in particular, deals with wave functions all the time.
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