[itishappy]

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.