I remember doing only simple (two-dimensional Euclidean) vectors before calculus -- length, scaling, addition, subtraction... Agreed that they obviously can get

I remember doing only simple (two-dimensional Euclidean) vectors before calculus -- length, scaling, addition, subtraction... Agreed that they obviously can get pretty hairy, but I don't think that side is exposed to people before calculus? Complex vector math was calculus III for myself.