It seems to me that most people think of a complex number A+Bi as different from the quaternion A+Bi+0j+0k. Reasons for this include: complex i has no more to do with the quaternion i than it has with j or k, and the quaternions are not a complex algebra in the usual sense (where a field commutes with all elements of any algebra over it).
But now I see that Mathematica identifies them. It will not simplify a+bI+cJ+dK to a+bI but it will treat the two as the same in operations.
Was I wrong, or is this just a meaningless side-effect of Mathematica's dislike for type rules?