Split-complex Number

A split-complex number is an ordered pair of real numbers, written in the form

where x and y are real numbers and the quantity j satisfies

Choosing results in the complex numbers. It is this sign change which distinguishes the split-complex numbers from the ordinary complex ones. The quantity j here is not a real number but an independent quantity; that is, it is not equal to ±1.

The collection of all such z is called the split-complex plane. Addition and multiplication of split-complex numbers are defined by

(x + j y) + (u + j v) = (x + u) + j(y + v)
(x + j y)(u + j v) = (xu + yv) + j(xv + yu).

This multiplication is commutative, associative and distributes over addition.

Read more about Split-complex Number:  Geometry, Algebraic Properties, Matrix Representations, History, Synonyms

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