 The biquaternions are then the complexification of the original (real) quaternions.Hamilton invented the term "associative" to distinguish between the imaginary scalar (known by now as a complex number) which is both commutative and associative, and four other possible roots of negative unity which he designated L, M, N and O, mentioning them briefly in appendix B of "Lectures on Quaternions" and in private letters.However, non-associative roots of minus one do not appear in "Elements of Quaternions".