Why is quaternion algebra 4D and not 3D? Complex algebra is 2D and what is known as quaternion algebra jumps to 4D.
$ i^2 = j^2 = k^2 = ijk = -1 $
Using $1, i, j,$ and $k$ as the base (where complex uses $1$ and $i$ (or $j$ if you are an EE)) which results in a 4-axis space. Why is there no 3D algebra?