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 [Formula: see text] matrix representation of Pauli quaternions. Moreover, we provide De Moivre’s formula for the light-like Pauli quaternions. Additionally, we give the [Formula: see text] roots of the matrix representation of Pauli quaternions. Moreover, we exemplify some of the results with illustrative examples to support the main formulas.

On Powers and Roots of Split Octonions

“…Terefore, it has been one of the important subjects studied after some fundamental operations in mathematics. Many studies have been carried out on the adaptation of the formula to the lots of number systems, which are the expansion of the complex number system (references [1][2][3][4][5][6][7] and therein). Split octonions have been worked on physics and mathematics [8][9][10][11][12][13][14][15][16][17][18][19][20].…”