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A Quaternion with Complex coefficients. The Algebra of biquaternions is isomorphic to a full matrix ring over the complex number field (van der Waerden 1985).
See also Quaternion
References
Clifford, W. K. ``Preliminary Sketch of Biquaternions.'' Proc. London Math. Soc. 4, 381-395, 1873.
Hamilton, W. R. Lectures on Quaternions: Containing a Systematic Statement of a New Mathematical Method.
Dublin: Hodges and Smith, 1853.
Study, E. ``Von den Bewegung und Umlegungen.'' Math. Ann. 39, 441-566, 1891.
van der Waerden, B. L. A History of Algebra from al-Khwarizmi to Emmy Noether.
New York: Springer-Verlag, pp. 188-189, 1985.