The matrices of Pauli quaternions, their De Moivre's and Euler's formulas

Abstract

In this paper, we obtain Euler's and De Moivre's formulas for the 4 x 4 matrix representation of Pauli quaternions. Moreover, we provide De Moivre's formula for the light-like Pauli quaternions. Additionally, we give the nth roots of the matrix representation of Pauli quaternions. Moreover, we exemplify some of the results with illustrative examples to support the main formulas.