> just vectors with special behavior for some operations > basically just a structure containing two real numbers and some modified behavior I think the issue

> just vectors with special behavior for some operations > basically just a structure containing two real numbers and some modified behavior I think the issue might be that you're brushing away what is central to their utility and interestingness? Yes, you can take the view that it's a 2D euclidean vector space but it's not just. It's a 2D commutative algebra over the reals, an algebraically closed field and its algebraic properties and the addition of a notion of a rotation operation to our concept of number is what's of central importance.