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In simple terms, the problem is distance functions are defined to give real numbers as answers, so you can't say i is a distance.
I don't think there is a generalization of distance functions to give complex numbers, as complex numbers cannot be (nicely) ordered, and thus don't make much sense to use as outputs of distance functions. Complex numbers are very useful in other areas though, and you can somewhat understand them as rotations.
I hope this makes sense, I tried to cut most technicalities, with all the downsides that has.
