17. M. John Wymelenberg, Three‐Dimensional Complex Analysis and Maxwell's Equations

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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