# Geometry of Generalized Complex Numbers

@article{Harkin2004GeometryOG, title={Geometry of Generalized Complex Numbers}, author={Anthony Harkin and Joseph B. Harkin}, journal={Mathematics Magazine}, year={2004}, volume={77}, pages={118 - 129} }

Alternative definitions of the imaginary unit i other than i2 = −1 can give rise to interesting and useful complex number systems. The 16th-century Italian mathematicians G. Cardan (1501–1576) and R. Bombelli (1526–1572) are thought to be among the first to utilize the complex numbers we know today by calculating with a quantity whose square is −1. Since then, various people have modified the original definition of the product of complex numbers. The English geometer W. Clifford (1845–1879…

## 69 Citations

HYBRID NUMBERS

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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 ( i = −1 ) , hyperbolic ( h = 1 ) and dual…

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In this study, we consider the generalized complex number system C_{p}={x+iy:x,y∈R,i²=p∈R} corresponding to elliptical complex number, parabolic complex number and hyperbolic complex number systems…

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In this paper, one-parameter planar motion in generalised complex plane (or p−complex plane) Cp = { x+ iy : x, y ∈ R, i = p } which is defined as a system of generalised complex numbers is studied.…

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