Abstract / Synopsis
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 transformation (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.
DOI
10.5642/jhummath.FRCK6517
Recommended Citation
Andrew W. Powell, "What is an Imaginary Number? The Plane and Beyond," Journal of Humanistic Mathematics, Volume 14 Issue 2 (July 2024), pages 264-285. DOI: 10.5642/jhummath.FRCK6517. Available at: https://scholarship.claremont.edu/jhm/vol14/iss2/9
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