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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