In my opinion this is the best answer, because it neatly explains why quaternions are more useful than vectors for rotation. Vectors are "nicer" because they ge

In my opinion this is the best answer, because it neatly explains why quaternions are more useful than vectors for rotation. Vectors are "nicer" because they generalize to arbitrary dimensions. But quaternions handle 3-dimensional rotations in (essentially) a single step. The point about interpolation is really important, because all the machinery offered by vectors becomes a burden. It's also good to think about complex numbers in the way described here because it neatly abstracts the concept of numbers and maps them to a form of dimensionality. Great comment all around.