Joe N says: >I'm saying present it as clearly as we know at this point - negative numbers are a combined concept - magnitude plus a direction.
I'll venture that if negative numbers were introduced this starkly, and old confusions consistently avoided, complex numbers could be made easily to seem just a another extension of the "numbers as incorporating combined concepts (perhaps more specifically, size and direction)" theme.
Here's a short list of things, points of contention perhaps, I've noted over the past several months. I'll not put names down.
1. Real numbers are really real somehow, but complex numbers really are fundamentally imaginary in some sense.
2. Whether defined or proven, the unit square *has* to end up as *the* unit of area measurement in 2D.
3. The usual sign rule (-) x (-) = (+), obscure as it is, just has to be.
I just see some vague pattern here. Anythings else to add to this list?