But none of that is related to my key point: multiplication by unitary values is significantly different depending on which axis the unit comes from (real vs im

But none of that is related to my key point: multiplication by unitary values is significantly different depending on which axis the unit comes from (real vs imaginary), hence my usage of 'asymmetric'. In the last part of my first comment I point out the benefit (that I perceive) arising from the asymmetry. I also still wonder if a symmetric version (like I describe in the first comment) would be possible. Splitting the geometric behavior into rotation, reflection, and scaling is interesting—so thanks for the description—I just don't see how it relates to my comment.