Complex numbers in 5 dimensions
| dc.creator | Olariu, Silviu | |
| dc.date | 2000-08-16 | |
| dc.date.accessioned | 2026-07-07T04:36:49Z | |
| dc.date.available | 2026-07-07T04:36:49Z | |
| dc.description | A system of commutative complex numbers in 5 dimensions of the form u=x_0+h_1x_1+h_2x_2+h_3x_3+h_4x_4 is described in this paper, the variables x_0, x_1, x_2, x_3, x_4 being real numbers. The operations of addition and multiplication of the 5-complex numbers introduced in this work have a geometric interpretation based on the the modulus d, the amplitude ρ, the polar angle θ_+, the planar angle ψ_1, and the azimuthal angles ϕ_1,ϕ_2. The exponential function of a 5-complex number can be expanded in terms of polar 5-dimensional cosexponential functions g_{5k}(y), k=0,1,2,3,4, and the expressions of these functions are obtained from the properties of the exponential function of a 5-complex variable. Exponential and trigonometric forms are obtained for the 5-complex numbers, which depend on the modulus, the amplitude and the angular variables. The 5-complex functions defined by series of powers are analytic, and the partial derivatives of the components of the 5-complex functions are closely related. The integrals of 5-complex functions are independent of path in regions where the functions are regular. The fact that the exponential form of the 5-complex numbers depends on the cyclic variables ϕ_1, ϕ_2 leads to the concept of pole and residue for integrals on closed paths. The polynomials of 5-complex variables can be written as products of linear or quadratic factors. | |
| dc.description | 18 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0008122 | |
| dc.identifier | http://arxiv.org/abs/math/0008122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59743 | |
| dc.subject | Complex Variables | |
| dc.subject | 30G35 (Primary) 32A45, 33E20, 46F15, 58J15 (Secondary) | |
| dc.title | Complex numbers in 5 dimensions | |
| dc.type | text |