I'm surprised at you fellas:
The whole point is that "i" or "j" is the Square Root of Minus One.
Thus minus i squared equals Plus One. So:
(2+i)*(2-i) = 4+1 = 5
(3+2i)*(3-2i) = 9+4 =13
Quaternions have 3 different square roots of -1, called i, j, k, and they too
have Complex Conjugates like Complex Numbers. The Imaginary Components i, j, k
then gave us the idea of Vectors. Divide two Vectors and you get a Quaternion.
Faictz Ce Que Vouldras: Frank Mitchell