Note that by the given definition, V _ \ parallel is a complex quantity.
3.
The basic idea is to use a real valued, it is convenient to define the complex quantities
4.
Where, \ varepsilon is a complex quantity and is a measure of departure from CP invariance.
5.
The action of the quaternionic matrices on quaternionic vectors is now represented by complex quantities, but otherwise it is the same as for " ordinary " matrices and vectors.
6.
In weak gravitational lensing, two different definitions are commonly used, and both are complex quantities which specify both the axis ratio and the position angle \ phi ~:
7.
The orders \ alpha _ k and \ beta _ k are in general complex quantities, but two interesting cases are when the orders are " commensurate"
8.
It is convenient that these two can be treated as the real and imaginary components of a complex quantity and use the Fourier theory to transform the measured time domain signal into the frequency domain representation.
9.
There is also an understood time dependence e ^ { i \ omega t } multiplying such phasor quantities; the actual field at a point in time and space is given by the real part of that complex quantity.
10.
Physical quantities may be expressed as complex numbers ( e . g . e ^ { i \ theta } ) which imply that the complex quantity has an orientation equal to that of the angle it is associated with ( in the above example ).
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