# Phasor **A [[complex number]] representing a [[Sinusoid|sinusoidal function]].** ![[Phasor.svg]] A **phasor**, a portmanteau of *phase [[vector]]*, is a complex number that represents a sinusoidal function with a time-invariant amplitude and initial phase and a constant [[angular frequency]]. > [!NOTE] Phasor > Let $f(t)=A\cos(\omega t+\phi)$ be a real-valued sinusoid with time-invariant amplitude $A$ and phase $\phi$ and a constant angular frequency $\omega$. > > The sinusoid can be represented as a single constant complex number, a **phasor**, multiplied by a factor dependent on time and frequency. > $A\cos(\omega t+\phi)+iA\sin(\omega t+\phi)=Ae^{i(\omega t+\phi)}=Ae^{i\phi}\cdot e^{i\omega t}$ Phasors are most commonly notated in [[Complex Number#Polar form|polar form]]. The magnitude of a phasor is equal to the amplitude of the sinusoid, while the argument is equal to the initial phase. Phasors exist within the *phasor* or *frequency domain* and mathematical operations between them require that the frequency remains consistent between the phasors and using either sine or cosine as the *zero phase reference*.