Complex numbers in 6 dimensions
| dc.creator | Olariu, Silviu | |
| dc.date | 2000-08-16 | |
| dc.date.accessioned | 2026-07-07T04:36:50Z | |
| dc.date.available | 2026-07-07T04:36:50Z | |
| dc.description | Two distinct systems of commutative complex numbers in 6 dimensions of the polar and planar types of the form u=x_0+h_1x_1+h_2x_2+h_3x_3+h_4x_4+h_5x_5 are described in this work, where the variables x_0, x_1, x_2, x_3, x_4, x_5 are real numbers. The polar 6-complex numbers introduced in this paper can be specified by the modulus d, the amplitude ρ, and the polar angles θ_+, θ_-, the planar angle ψ_1, and the azimuthal angles ϕ_1, ϕ_2. The planar 6-complex numbers introduced in this paper can be specified by the modulus d, the amplitude ρ, the planar angles ψ_1, ψ_2, and the azimuthal angles ϕ_1, ϕ_2, ϕ_3. Exponential and trigonometric forms are given for the 6-complex numbers. The 6-complex functions defined by series of powers are analytic, and the partial derivatives of the components of the 6-complex functions are closely related. The integrals of polar 6-complex functions are independent of path in regions where the functions are regular. The fact that the exponential form of ther 6-complex numbers depends on cyclic variables leads to the concept of pole and residue for integrals on closed paths. The polynomials of polar 6-complex variables can be written as products of linear or quadratic factors, the polynomials of planar 6-complex variables can always be written as products of linear factors, although the factorization is not unique. | |
| dc.description | 27 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/0008123 | |
| dc.identifier | http://arxiv.org/abs/math/0008123 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59744 | |
| dc.subject | Complex Variables | |
| dc.subject | 30G35 (Primary) 32A45, 33E20, 46F15, 58J15 (Secondary) | |
| dc.title | Complex numbers in 6 dimensions | |
| dc.type | text |