What was not obvious to me, and took a lot of higher math to get to, was that in the grouping of N=>I=>Q=>R=>C, at each stage you're pulling in a more complete mathematical representation (counting, rings, fields) until you're algebraically closed, and while you could go higher, you start losing properties you like again, like commutability over multiplication.

Complex numbers are that nice saddle point, which is an interesting thing to ponder.

I wish there was more focus on these "why" aspects in at least the optional advanced math or physics you could get in HS. It helps put some things in perspective.