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.