# Transformations of Complex, Dual, and Hyperbolic Numbers

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This Demonstration compares the multiplicative transformation properties on the plane of complex, dual, and hyperbolic numbers. These number types share the form , where and are real numbers and has the defining characteristics: for complex numbers, for dual numbers, and for hyperbolic numbers. Their conjugates share the form and their modulus the form The figure shows, for the selected number type,

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Contributed by: Fred Klingener (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Hyperbolic numbers (sometimes called split-complex numbers) are useful for measuring distances in the Lorentz space-time plane (see G. Sobczyk, "The Hyperbolic Number Plane," *The College Mathematics Journal*, 26(4), 1995 pp. 268–280).

## Permanent Citation

"Transformations of Complex, Dual, and Hyperbolic Numbers"

http://demonstrations.wolfram.com/TransformationsOfComplexDualAndHyperbolicNumbers/

Wolfram Demonstrations Project

Published: March 7 2011