The Euler's formula and root formula of Clifford Algebra Cl2

TL;DR

This paper extends Euler's and De Moivre's formulas to Clifford algebra Cl2 and derives methods to compute nth roots of elements within this algebra, broadening the algebraic tools available for Clifford algebra analysis.

Contribution

It introduces explicit Euler's and De Moivre's formulas for Clifford algebra Cl2 and provides a procedure to find nth roots of elements, which is a novel extension in this algebraic context.

Findings

Euler's formula for Cl2 derived

De Moivre's formula for Cl2 established

Method for nth roots in Cl2 developed

Abstract

In this paper, we express Euler's formula and De Moivre's formula for Clifford algebra Cl2 and find nth roots of an element in Clifford algebra Cl2.