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
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 .