Roy Lewallen wrote in
:

A phasor is a replacement of cos(omega * t + phi) with cos(omega * t +
phi) + j * sin(omega * t + phi) = exp(j * (omega * t + phi)) = exp(j *
omega * t) * exp(j * phi). The first of those quantities is understood
but not generally written in phasor analysis, but is nonetheless an
essential part of the definition of a phasor. This shows that a phasor
is a vector which rotates in the complex plane, with a rotational speed
of omega * t radians/sec. The reason the time-dependent rotational term

Should that be ...of omega radians/sec..., omega*t is the phase
displacement, omega is the phase velocity?

Owen