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

**B** = **B**_{Re} + *i*·**B**_{Im}.

The canonical form for the complex vector is:
**B** = ·*e*^{iφ},

where

φ - phase,

*B*_{x} and *B*_{y} are real components of the magnitude vector, and

*k* is a coefficient of polarization (-1≤k≤1).

Coefficient of polarization is *k* = *B*_{min} / *B*_{max}.
*k*=0 corresponds to linear polarization along the direction defined by the vector (*B*_{x}, *B*_{y}). The *k*=1 corresponds to the counterclockwise circular polarization, *k*=-1 corresponds to the clockwise circular polarization.

*B*_{max} = 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: *B*_{RMS} =

**Related Topics**

Complex Value.