Complex Vectors in Magnetoionic Theory

ABSTRACT

In the electromagnetic theory of harmonic waves in linear systems, the various field quantities are often represented by complex numbers which contain the time t through a factor e^iωt. Then the electric and magnetic field vectors are complex vectors, and in general may be thought of as having complex lengths and directions. If the instantaneous field associated with a complex vector E is drawn as a real vector with a fixed origin, its end point traverses an ellipse whose features can be expressed in terms of the scalar and vector products of E with itself or with its complex conjugate. Some applications of this to the design of aerials for space vehicles, and to the relations between the electric and magnetic fields in magnetoionic theory are discussed.