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Quaternion polar representation with a complex modulus and complex argument inspired by the Cayley-Dickson form

Sangwine, SJ and Bihan, NL (2010) 'Quaternion polar representation with a complex modulus and complex argument inspired by the Cayley-Dickson form.' Advances in Applied Clifford Algebras, 20 (1). 111 - 120. ISSN 0188-7009

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Abstract

We present a new polar representation of quaternions inspired by the Cayley-Dickson representation. In this new polar representation, a quaternion is represented by a pair of complex numbers as in the Cayley-Dickson form, but here these two complex numbers are a complex 'modulus' and a complex 'argument'. As in the Cayley-Dickson form, the two complex numbers are in the same complex plane (using the same complex root of - 1), but the complex phase is multiplied by a different complex root of - 1 in the exponential function. We show how to calculate the 'modulus' and 'argument' from an arbitrary quaternion in Cartesian form. © 2008 Birkhäuser Verlag Basel/Switzerland.

Item Type: Article
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QC Physics
Divisions: Faculty of Science and Health > Computer Science and Electronic Engineering, School of
Depositing User: Jim Jamieson
Date Deposited: 05 Mar 2013 13:36
Last Modified: 30 Jan 2019 16:16
URI: http://repository.essex.ac.uk/id/eprint/5560

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