I'm wrong. Too late to edit, correction below: quaterions: a*1 + b*i + c*j + d*k rotors: a*1 + b*xy + c*yz + d*zx The representations I share

I'm wrong. Too late to edit, correction below: quaterions: a*1 + b*i + c*j + d*k rotors: a*1 + b*xy + c*yz + d*zx The representations I shared previously with zero real component are for the points under rotation, not the rotors themselves which have real components in the general form. Apologies for misinformation! The exceptions are 0 degrees and 180 degree rotations (and 360, 540, etc...), which will have one and zero as the real components, respectively.