But that is hardly a ‘natural occurence’ of complex numbers - it just turned out that they were useful to represent the special case of harmonic solutions because of their relationship with trig functions.
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The natural representation would be the transient solution u(t) or i(t). Harmonic solutions are merely a special case, for which it turned out complex numbers were useful (because of the way they can represent rotation). They certainly serve a purpose there, but imo this is not an instance of ‘complex numbers appearing in nature’.