A hypercomplex number is an element of a finite-dimensional algebra over the real numbers that is unital and distributive (but not necessarily associative).

A hypercomplex number is an element of a finite-dimensional algebra over the real numbers that is unital and distributive (but not necessarily associative). Elements are generated with real number coefficients $(a_0, \dots, a_n)$ for a basis $\{ 1, i_1, \dots, i_n \}$. Where possible, it is conventional to choose the basis so that $i_k^2 \in \{ -1, 0, +1 \}$. A technical approach to hypercomplex numbers directs attention first to those of dimension two. Higher dimensions are configured as Cliffordian or algebraic sums of other algebras and are usually obtained with the Cayley-Dickson's construction.