Quaternions

Complex numbers were invented to solve x^2 +1 = 0
Quaternions where invented for ???????

>>8
Polynomials with real coefficients modulo x^2+1.  So essentially you work with polynomials instead of numbers, but you set x^2+1 to be zero.  So for instance

x^3+x+1 = x*(x^2+1)+1 = x*0+1 = 1

Search for "modular arithmetic" on wiki.  It's not the exact same thing, but the general idea is the same.