As a non-math person, I've thought a lot about quaternions and why they need 4 dimensions, and why there aren't 3d complex numbers. It's because if you think ab

As a non-math person, I've thought a lot about quaternions and why they need 4 dimensions, and why there aren't 3d complex numbers. It's because if you think about it, on the complex plane, the imaginary number i just represents a rotation of 90 degrees. Now if you think about a 3d space, i represents a rotation across one dimension, and j represents a rotation across another dimension. But how do you rotate from i to j? You can't without another number k.