‘Clifford Algebra’ Complex Numbers For 3-D Vector Representation

Abstract

The use of quaternions has historically been an approach to extend complex numbers to represent 3-D vectors. This quaternion representation is not unique. It is shown that an alternative approach to such an extension is to define complex numbers obeying a Clifford algebra different from those of quaternions. Such an algebra is not new but appears to be preferable and less likely to cause confusion.