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Volume 12: Pages 383-389, 1999
Three‐Dimensional Complex Analysis and Maxwell's Equations
M. John Wymelenberg
2500 California Plaza, Omaha, NE 68178‐0522 U.S.A.
The author attempts to discover a method of working with three‐dimensional vectors and potential that is more amenable to ordinary mathematics. Conventional vector analysis relies upon rules a little different from those of ordinary mathematics. There is consequently a difficulty, for example, when establishing a proof that involves derivatives. Imaginary coefficients, inherent to ordinary mathematics, would seem to provide an answer. Quaternions make use of these imaginary coefficients, but this discipline is quite unwieldy. A seemingly satisfactory method has been found which, as an example of its usefulness, has been used to derive Maxwell's equations.
Keywords: imaginary or complex coefficients, complex vector, complex coordinate, complex potential, Maxwell's equations
Received: May 7, 1999; Published online: December 15, 2008