What is an imaginary number? The plane and beyond
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Published version
Author(s)
Powell, Andrew W
Type
Journal Article
Abstract
In this article I argue that i is a quantity associated with the two-dimensional real number plane, whether as a vector, a bi-vector, a point or a transforma tion (rotation). This position provides a foundation for the complex numbers
and accounts for complex numbers in some equations of applied mathematics and physics. I also argue that complex numbers are fundamentally geometrical
and can be described by geometric algebra, and that moreover the meaning of complex numbers in physics varies with dimension and geometry of the manifold.
Keywords: complex numbers, geometric algebra, imaginary number, spacetime algebra, split complex numbers.
and accounts for complex numbers in some equations of applied mathematics and physics. I also argue that complex numbers are fundamentally geometrical
and can be described by geometric algebra, and that moreover the meaning of complex numbers in physics varies with dimension and geometry of the manifold.
Keywords: complex numbers, geometric algebra, imaginary number, spacetime algebra, split complex numbers.
Date Issued
2024-07-01
Date Acceptance
2024-07-01
Citation
Journal of Humanistic Mathematics, 2024, 14 (2), pp.264-285
ISSN
2159-8118
Publisher
Claremont Colleges Library
Start Page
264
End Page
285
Journal / Book Title
Journal of Humanistic Mathematics
Volume
14
Issue
2
Copyright Statement
©2024 by the authors. This work is licensed under a Creative Commons License.
License URL
Identifier
https://doi.org/10.5642/jhummath.frck6517
Publication Status
Published
Date Publish Online
2024-07-01