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Volume :38 Issue : 1 2011      Add To Cart                                                                    Download

De Moivre’s formula for dual quaternions

Auther : HESNA KABADAYI* AND YUSUF YAYLI**

*Department of Mathematics, Ankara university, 06100 Tandod\breve gan - Ankara, Turkey

e-mail: kabadayi@science.ankara.edu.tr

**Department of Mathematics, Ankara university, 06100 Tandod\breve gan - Ankara, Turkey

e-mail:yayli@science.ankara.edu.tr

ABSTRACT

By E. Cho (1998), Eulers formula and De Moivres formula are given for real quaternions and existence of uncountably many unit quaternions satisfying xn=1 for n ≥ 3 is shown.

In this paper, first of all geometrical interpretation of unit dual quaternions is given and unit dual quaternions are shown to work as screw operators, and group structures of these are given. Moreover, De Moivres formula and Eulers formula for dual quaternions are obtained. Lastly, solutions of the equation xn=1 is discussed and while the equation xn =1 has uncountably many solutions for real quaternions, it is shown not to have solutions for a general unit dual quaternion.

Keywords: De Moivre; Dual quaternion; Euler; Screw motion.

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