Abstract：In this paper， by means the concept of split quaternions， firstly， the algebraic properties of split quaternions are given. Secondly， the de Moivre's formula and Euler's formula for split quaternions in two different cases are obtained. Furthermore， according to the de Moivre's formula， the rooted theorem of split quaternion equation is obtained， and the formula for finding the arbitrary powers of split quaternions are obtained， and the relations between the different powers of split quaternions are studied. Finally， the de Moivre's formula of the real representation matrix of split quaternions are obtained. The correctness and validity of the conclusion are verified by numerical examples.
2021, Vol. 55 
