I personally believe it is still a nonsense, wrt the "special case" (your literal words) bit: do not misunderstand me! I am too hoping that -to quote you verbatim- we "could use the special type for all sorts of vector math, tensors, quadratics, values with units attached." (And more!) Nevertheless, complex numbers are something more: i.e. a field, and that cannot be told of general n-dimensional vector spaces: given the confidence you talk about these topics, you certainly know that the only three real algebras (with division) are the reals themselves, the complex numbers and quaternions. (Then you have the more esoteric Cayley numbers, if you're willing to give up on associativity.) Or else, are you taking, say, two n-dimensional vectors and multiply them together?!? Certainly, you can have an inner product, but that's an entirely different beast, and not a generalization of complex multiplication. Thus, definitely, not as a "special case."
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