There are three imaginary vectors, i, j and k. The complement of a quaternion flips the sign of the these vectors. Both of these can be split into even and odd parts. Two of these fancy multiplications are actually quite familiar. If only real numbers are used, there is no difference between any Grassman and Euclidean products, and all odd products are zero.
Identical statements apply to the divisions.
I reserve all rights to this software. Visit and play as you like, but if you want to use the engine behind this for 3D animations, let's talk.