Abstract
In this study, we define a new non-commutative number system called hybrid numbers. This number system can be accepted as a generalization of the complex $$\left( {\mathbf {i}}^{2}=-1\right) $$ , hyperbolic $$\left( {\mathbf {h}} ^{2}=1\right) $$ and dual number $$\left( \varvec{\varepsilon }^{2}=0\right) $$ systems. A hybrid number is a number created with any combination of the complex, hyperbolic and dual numbers satisfying the relation $$\mathbf { ih=-hi=i}+\varvec{\varepsilon }.$$ Because these numbers are a composition of dual, complex and hyperbolic numbers, we think that it would be better to call them hybrid numbers instead of the generalized complex numbers. In this paper, we give some algebraic and geometric properties of this number set with some classifications. In addition, we examined the roots of a hybrid number according to its type and character.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
