### Quaternions #### Like Complex Numbers, but for 3D $$ q = e^{B\theta}=\mbox{cos}\theta+B\mbox{sin}\theta $$ $$ B = ix + jy + kz $$ $$ i^2 = j^2 = k^2 = ijk = -1 $$ $$ ij = -ji = k $$ $$ jk = -kj = i $$ $$ ki = -ik = j $$