Sangwine, SJ and Bihan, NL (2010) 'Quaternion polar representation with a complex modulus and complex argument inspired by the CayleyDickson form.' Advances in Applied Clifford Algebras, 20 (1). 111  120. ISSN 01887009

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Abstract
We present a new polar representation of quaternions inspired by the CayleyDickson representation. In this new polar representation, a quaternion is represented by a pair of complex numbers as in the CayleyDickson form, but here these two complex numbers are a complex 'modulus' and a complex 'argument'. As in the CayleyDickson 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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