Biquaternion (complexified quaternion) roots of -1

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dc.creatorSangwine, Stephen J.
dc.date2005-06-10
dc.date.accessioned2026-07-07T06:29:20Z
dc.date.available2026-07-07T06:29:20Z
dc.descriptionThe 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.
dc.identifierhttps://arxiv.org/abs/math/0506190
dc.identifierhttp://arxiv.org/abs/math/0506190
dc.identifierAdvances in Applied Clifford Algebras, 16 (1), February 2006, 63-68.
dc.identifierdoi:10.1007/s00006-006-0005-8
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97995
dc.subjectRings and Algebras
dc.subject11R52
dc.titleBiquaternion (complexified quaternion) roots of -1
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