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Year 2019, , 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, , 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

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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