De Moivre's Theorem of Hyperbolic Real Split Quaternions
Based on the concept of the hyperbolic real split quaternion,firstly,the related properties of hyperbolic real split quaternion are given.Secondly,by using the polar representation of the hyperbolic real split quaternion,the De Moivre's theorems of the hyperbolic real split quaternion in three cases are obtained,and the Euler's formula is extended.Thirdly,using the obtained De Moivre's theorem,the root-finding formula of the hyperbolic real split quaternion equation is given.Finally,the relationship between different powers of the hyperbolic real split quaternion in special cases is discussed.The correctness of the conclusions are verified by some examples.
hyperbolic real split quaternionDe Moivre's theorempolar representationEuler's formula
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