Biquaternion (complexified quaternion) roots of -1

Details Biquaternion (complexified quaternion) roots of -1 Biquaternion (complexified quaternion) roots of -1

2005-06-10

arxiv.org/abs/math/0506190v1

Advances in Applied Clifford Algebras, 16 (1), February 2006, 63-68.

Mathematics

Rings and Algebras

Scientific paper

10.1007/s00006-006-0005-8

The roots of -1 in the set of biquaternions (quaternions with complex components, or complex numbers with quaternion real and imaginary parts) are studied and it is shown that there is an infinite number of non-trivial complexified quaternion roots (and two degenerate solutions which are the complex imaginary operator and the set of unit pure real quaternions). The non-trivial roots are shown to consist of complex numbers with perpendicular pure quaternion real and imaginary parts. The moduli of the two perpendicular pure quaternions are expressible by a single parameter via a hyperbolic trigonometric identity.

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