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.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: March 13, 2008. Accepted: July 2, 2008.
Rights and permissions
About this article
Cite this article
Sangwine, S.J., Bihan, N.L. Quaternion Polar Representation with a Complex Modulus and Complex Argument Inspired by the Cayley-Dickson Form. AACA 20, 111–120 (2010). https://doi.org/10.1007/s00006-008-0128-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00006-008-0128-1