Square roots of complexified quaternions

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.