Quaternions

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

>>5
You never *need* to use complex numbers to prove things about real numbers, since you can always rewrite proofs to use the ring \mathbb{R}[x]/(x^2+1) instead, which is isomorphic to \mathbb{C} and doesn't actually require imaginary numbers to define and use.