IMO there is nothing “natural” in interpreting complex numbers as a vector. The fact you get a thing out of them that looks a lot like a vector is one of the st

IMO there is nothing “natural” in interpreting complex numbers as a vector. The fact you get a thing out of them that looks a lot like a vector is one of the stupefying ‘mysteries’ of math which make the discipline so cool. Complex numbers afaik began as an attempt to solve polynomial equations. They begin from the agreement to invent a number i whose square is -1 so you can solve equations having sqrt(-1) in them. The jump from sqrt(-1) to plane rotations is to my feeble mind one of the most flabbergastingly unintuitive things in ‘basic’ maths. “A rotation you say? Who ordered that!?”