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Complex Vector

A pair of real vectors - one as a real part and the second as an imaginary part defines the Complex Vector.

B = BRe + i·BIm.

The canonical form for the complex vector is:
B = ·e,
where
   φ - phase,
   Bx and By are real components of the magnitude vector, and
   k is a coefficient of polarization (-1≤k≤1).

Coefficient of polarization is k = Bmin / Bmax.
k=0 corresponds to linear polarization along the direction defined by the vector (Bx, By). The k=1 corresponds to the counterclockwise circular polarization, k=-1 corresponds to the clockwise circular polarization.

Bmax = is a real magnitude of the complex vector, it corresponds to the maximum momentary value of time-dependent B.

RMS value of complex vector is: BRMS =

Related Topics
Complex Value.