Numbers can have more than one imaginary component {hypercomplex number} {hypernumber}. Complex numbers are two-dimensional vectors, and hypernumbers are n-dimensional vectors. Hypernumbers can represent tensors, quaternions, matrices, determinants, and all number types. Hypernumbers are directed line segments {extension, calculus}.
magnitude
Magnitudes are the same as for vectors.
addition
Hypernumbers add corresponding parts, like complex numbers.
multiplication
Hypernumbers, like complex numbers, multiply like polynomials. Products are scalars or vectors. Product of same axis and itself makes scalars. When axis multiplies another axis, result is vector orthogonal to both original axes.
Mathematical Sciences>Number Theory>Number Types>Complex Number>Hypercomplex
3-Number Theory-Number Types-Complex Number-Hypercomplex
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Date Modified: 2022.0224