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Square roots of complexified quaternions

Mathematical Physics 2026-03-17 v2 math.MP

Abstract

Square roots of complexified (complex) quaternions, namely, the Hamilton quaternion, coquaternion, nectorine, and conectorine are investigated. The isomorphisms between the complex quaternions and 3-dimensional multivectors of Clifford algebras is employed for this purpose. Root examples for all named quaternions are presented from which follows that the complex quaternionic roots may assume discrete or continuous form, or there may be no roots at all.

Cite

@article{arxiv.2601.08391,
  title  = {Square roots of complexified quaternions},
  author = {Adolfas Dargys and Arturas Acus},
  journal= {arXiv preprint arXiv:2601.08391},
  year   = {2026}
}

Comments

16 pages, 1 algorithm

R2 v1 2026-07-01T09:02:29.989Z