Phasor

A phasor is the complex phase of a sine wave of constant angular frequency and time-invariant amplitude. Given a complex sine wave

ψ(x,t)=Aei[k⋅r−ωt+φ]\psi(x,t)=Ae^{i[\mathbf{k}\cdot \mathbf{r}-\omega t+\varphi]}

where ω\omega is constant, the term

AeiφAe^{i\varphi}

is called the phasor of the wave.

The name comes from the portmanteau of "phase" and "vector", but it is a bit of a misnomer. Phasors are not vectors: their set does not form a Vector space. However, some properties of vectors do apply, most important of which is that they sum in the same way as vectors. This allows for greatly simplified calculation of wave superposition as operations that would be quite complicated in non-phasor notation become relatively simple algebraic equations when in phasor notation.