Hypercomplex numbermathematics, hypercomplex numbers are extensions of the complex numbers constructed by means of abstract algebra, such as quaternions, octonions and sedenions.
Whereas complex numbers can be viewed as points in a plane, hypercomplex numbers can be viewed as points in some higher-dimensional Euclidean space (4 dimensions for the quaternions, 8 for the octonions, 16 for the sedenions). More precisely, they form finite-dimensional algebras over the real numbers. But none of these extensions forms a field, essentially because the field of complex numbers is algebraically closed — see fundamental theorem of algebra.
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