Ah, I missed this. I should pay more attention! I used to post many maths problems. Good to see some new ones - especially with a little twist. I don't think I would have summoned the quaternion solution, although having got that far we could go all the way with the infinite number of solutions afforded by the exponential notation and adding n.2pi radians.

Oh yeah, you got a random upvote! That's how I found the post.