QUATERNION NUMBERS TO ' PLATE SOLVING THE QUADRATIC EQUATION

Authors

  • Mamajonov JD Physics Mathematics Sciences Doctor (DSc ) , Fergana State University , Associate Professor
  • Ismailov.MX Farg is a Mother State University _ Teacher
  • Mukhtorov T.Sh. Farg is a mother state university , graduate student

Keywords:

imaginary unit, guiding vectors, quaternion numbers, distribution property, biquadratic equation, infinitely many, square root.

Abstract

The quadratic equation is solved using the operations defined in the set of quarternion numbers. The quadratic equation was solved in a special case, and its roots were found. The theorem on the solution of the quadratic equation is given, the formula for finding the square
root of the number of quarternions is given.

References

Gordeev V.N. Quaternions and biquaternions with applications in geometry and mechanics// Kiev. Stal Publishing House, 2016.316 p . https://www.researchgate.net/publication/326377622

N. S. Polyakov .. Differentiation of functions of a quaternion variable // Chebishevsky collection 2019, vol. 20, issue 2, p. 298-310.DOI: https://doi.org/10.22405/2226-8383-2018-20-2-298-310

Branets A. V., Shmyglevsky I. P. Application of quaternions in problems of orientation of a rigid body / A.V. Branets , I.P. Shmyglevsky // Moscow, Nauka, 1973, 320 p.https://rusneb.ru/catalog/000219_000011

Kletenik D.V. Collection of problems in analytical geometry /D.V. Kletenik // Moscow, Science,Fizmatlit , 1998, 240 s http://elib.kstu.kz/fulltext/skan/Kletenik.

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Published

2023-02-18

Issue

Vol. 11 No. 2 (2023): GIIRJ

Section

Articles

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