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Year 2019, Volume: 2 Issue: 3, 126 - 129, 30.09.2019
https://doi.org/10.32323/ujma.587816

Abstract

References

  • [1] D. P. Mandic, V. S. L. Goh, Complex valued nonlinear adaptive filters: noncircularity, widely linear and neural models, John Wiley Sons, 2009.
  • [2] W. K. Clifford, Preliminary sketch of bi-quaternions, Proc. London Math. Soc., 4(1873), 381-395.
  • [3] E.Study, Geometrie der Dynamen, Leipzig, Germany, 1903.
  • [4] I. M. Yaglom, A Simple Non-Euclidean Geometry and Its Physical Basis, Springer-Verlag New York, 1979.
  • [5] S. Y¨uce, Z. Ercan, On Properties of the Dual Quaternions, Eur. J. Pure Appl. Math., 4(2)(2011), 142-146.
  • [6] G. Helzer, Special Relativity with acceleration, Amer. Math. Monthy, 107(3)(2000), 219-237.
  • [7] E. Cho, De-Moivre’s formula for quaternions, Appl. Math. Lett. 11(6)(1998), 33-35.
  • [8] H. Kabadayı, Y. Yaylı, De-Moivre’s formula for dual quaternions, Kuwait J. Sci. Tech, 38(1)(2011), 15-23.
  • [9] I. A. K¨osal, A note on hyperbolic quaternions, Univers. J. Math. Appl., 1(3)(2018), 155-159.
  • [10] V. Majernik, Multicomponent number systems, Acta Phys. Polon. A, 3(90)(1996), 491-498.
  • [11] F. Messelmi, Dual-Complex Numbers and Theır Holomorphic Functions, https://hal.archives-ouvertes.fr/hal-01114178, (2015).

De-Moivre and Euler Formulae for Dual-Complex Numbers

Year 2019, Volume: 2 Issue: 3, 126 - 129, 30.09.2019
https://doi.org/10.32323/ujma.587816

Abstract

In this study, we generalize the well-known formulae of De-Moivre and Euler of complex numbers to dual-complex numbers. Furthermore, we investigate the roots and powers of a dual-complex number by using these formulae. Consequently, we give some examples to illustrate the main results in this paper.

References

  • [1] D. P. Mandic, V. S. L. Goh, Complex valued nonlinear adaptive filters: noncircularity, widely linear and neural models, John Wiley Sons, 2009.
  • [2] W. K. Clifford, Preliminary sketch of bi-quaternions, Proc. London Math. Soc., 4(1873), 381-395.
  • [3] E.Study, Geometrie der Dynamen, Leipzig, Germany, 1903.
  • [4] I. M. Yaglom, A Simple Non-Euclidean Geometry and Its Physical Basis, Springer-Verlag New York, 1979.
  • [5] S. Y¨uce, Z. Ercan, On Properties of the Dual Quaternions, Eur. J. Pure Appl. Math., 4(2)(2011), 142-146.
  • [6] G. Helzer, Special Relativity with acceleration, Amer. Math. Monthy, 107(3)(2000), 219-237.
  • [7] E. Cho, De-Moivre’s formula for quaternions, Appl. Math. Lett. 11(6)(1998), 33-35.
  • [8] H. Kabadayı, Y. Yaylı, De-Moivre’s formula for dual quaternions, Kuwait J. Sci. Tech, 38(1)(2011), 15-23.
  • [9] I. A. K¨osal, A note on hyperbolic quaternions, Univers. J. Math. Appl., 1(3)(2018), 155-159.
  • [10] V. Majernik, Multicomponent number systems, Acta Phys. Polon. A, 3(90)(1996), 491-498.
  • [11] F. Messelmi, Dual-Complex Numbers and Theır Holomorphic Functions, https://hal.archives-ouvertes.fr/hal-01114178, (2015).
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mehmet Ali Güngör 0000-0003-1863-3183

Ömer Tetik This is me

Publication Date September 30, 2019
Submission Date July 5, 2019
Acceptance Date September 5, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

APA Güngör, M. A., & Tetik, Ö. (2019). De-Moivre and Euler Formulae for Dual-Complex Numbers. Universal Journal of Mathematics and Applications, 2(3), 126-129. https://doi.org/10.32323/ujma.587816
AMA Güngör MA, Tetik Ö. De-Moivre and Euler Formulae for Dual-Complex Numbers. Univ. J. Math. Appl. September 2019;2(3):126-129. doi:10.32323/ujma.587816
Chicago Güngör, Mehmet Ali, and Ömer Tetik. “De-Moivre and Euler Formulae for Dual-Complex Numbers”. Universal Journal of Mathematics and Applications 2, no. 3 (September 2019): 126-29. https://doi.org/10.32323/ujma.587816.
EndNote Güngör MA, Tetik Ö (September 1, 2019) De-Moivre and Euler Formulae for Dual-Complex Numbers. Universal Journal of Mathematics and Applications 2 3 126–129.
IEEE M. A. Güngör and Ö. Tetik, “De-Moivre and Euler Formulae for Dual-Complex Numbers”, Univ. J. Math. Appl., vol. 2, no. 3, pp. 126–129, 2019, doi: 10.32323/ujma.587816.
ISNAD Güngör, Mehmet Ali - Tetik, Ömer. “De-Moivre and Euler Formulae for Dual-Complex Numbers”. Universal Journal of Mathematics and Applications 2/3 (September 2019), 126-129. https://doi.org/10.32323/ujma.587816.
JAMA Güngör MA, Tetik Ö. De-Moivre and Euler Formulae for Dual-Complex Numbers. Univ. J. Math. Appl. 2019;2:126–129.
MLA Güngör, Mehmet Ali and Ömer Tetik. “De-Moivre and Euler Formulae for Dual-Complex Numbers”. Universal Journal of Mathematics and Applications, vol. 2, no. 3, 2019, pp. 126-9, doi:10.32323/ujma.587816.
Vancouver Güngör MA, Tetik Ö. De-Moivre and Euler Formulae for Dual-Complex Numbers. Univ. J. Math. Appl. 2019;2(3):126-9.

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