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

The heart of the preceding proof was the algebraic manipulation

The 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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