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On the Three Types of Complex Number and Planar Transformations

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  • J Rooney

    (School of Automotive Studies, Cranfield Institute of Technology, Cranfield, Bedford, MK43 OAL, England)

Abstract

This paper compares the three possible types of complex number. These provide a very concise means for representing certain geometric transformations of the points of a plane. The first type considered is the ordinary complex number, a + i b (where i 2 = −1). This is used in the exponential form exp(iα) to rotate the plane through the angle α. The second type is the dual number, a + ∈b (where ∈ 2 = 0), and exp( ∈τ ) shears the plane parallel to the y -axis through the shear τ. The third type is the double number, a + j b (where j 2 = +1), and exp(jβ) represents another type of shear transformation, known as a Lorentz transformation, which shears the plane through the rapidity β.

Suggested Citation

  • J Rooney, 1978. "On the Three Types of Complex Number and Planar Transformations," Environment and Planning B, , vol. 5(1), pages 89-99, June.
    • Handle: RePEc:sae:envirb:v:5:y:1978:i:1:p:89-99
    DOI: 10.1068/b050089
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