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The Phasor is an extremely important concept in engineering analysis. It provides a very convenient and compact representation of steady-state, single-frequency, sinusoidally varying waveforms.

Assume that some waveform is of the form:

v(t) = A * cos(wt + Θ)

or since e j X = cos(X) + j * sin(X)

v(t) = Real ( A * e j(wt + Θ) )

In linear systems, any system that has a forcing fuction which follows the form of v(t) from above will also have solutions which contain the exponential term e jwt. This term is typically removed from the equations for simplicity sake; the remaining term, containing the phase angle of the particular waveform, e j Θ, is kept. This remaining term is called a Phasor. Phasors are immensely useful since they may be represented vectorially in the complex plane, i.e.

v(t) = e j Θ = cos(Θ) + j * sin(Θ)

An additions and subtractions of Phasors may be carried out in a vector fashion.

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