### Phasor Analysis: Factoring a Complex Sinusoid into Phasor Times Carrier

The heart of the preceding proof was the algebraic manipulation

*carrier term*``factors out'' of the sum. Inside the sum, each sinusoid is represented by a complex constant , known as the

*phasor*associated with that sinusoid.

For an arbitrary sinusoid having amplitude , phase , and radian frequency , we have

re

Thus, a sinusoid is determined by its frequency (which
specifies the carrier term) and its phasor
,
a complex constant. Phasor analysis is discussed further in
[84].

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Proof Using Complex Variables