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Article Dans Une Revue Advances in Applied Clifford Algebras Année : 2010

Quaternion Polar Representation with a Complex Modulus and Complex Argument Inspired by the Cayley-Dickson Form

Résumé

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.

Dates et versions

hal-00515650 , version 1 (07-09-2010)

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Stephen Sangwine, Nicolas Le Bihan. Quaternion Polar Representation with a Complex Modulus and Complex Argument Inspired by the Cayley-Dickson Form. Advances in Applied Clifford Algebras, 2010, 20 (1), pp.111-120. ⟨10.1007/s00006-008-0128-1⟩. ⟨hal-00515650⟩
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