8 papers · 1 filter
Complex Numbers in n Dimensions
Silviu Olariu
This monograph presents a detailed analysis of hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions. It continu…
Planar complex numbers in even n dimensions
Silviu Olariu
Planar commutative n-complex numbers of the form u=x_0+h_1x_1+h_2x_2+...+h_{n-1}x_{n-1} are introduced in an even number n of dimensions, the variables x_0,...,x_{n-1} being real n…
Polar complex numbers in n dimensions
Silviu Olariu
Polar commutative n-complex numbers of the form u=x_0+h_1x_1+h_2x_2+...+h_{n-1}x_{n-1} are introduced in n dimensions, the variables x_0,...,x_{n-1} being real numbers. The polar n…
Complex numbers in 6 dimensions
Silviu Olariu
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, w…
Complex numbers in 5 dimensions
Silviu Olariu
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 n…
Commutative complex numbers in four dimensions
Silviu Olariu
Commutative complex numbers of the form u=x+αy+βz+γt in 4 dimensions are studied, the variables x, y, z and t being real numbers. Four distinct types of multiplication rules for th…