Charles M. Close in "The Analysis of Linear Circuits" has this
footnote in a section called Representing Sinusoidal Function of Time:

"Although directed lines are commonly called vectors, this terminology
is avoided in this application. In field theory, quantities that have
an orientation in three-dimensional space and that are sinusoidal
functions of time are encountered. The term "vector" then refers to
the spacial orientation, and the term "rotating phasor" to the
exponential terms [Fe^jwt and its complex conjugate]. Since both
phasors and vectors are complex quantities, phasors are added and
subtracted in the same way as vectors."

According to the text, since the two complex functions of t in
exponential form can be graphically represented as directed lines, and
since each is the conjugate of the other, they are called
counter-rotating phasors. They each make w/2pi revolutions per second
and have an angular frequency of w radians per second.

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Richard Harrison wrote:
Cecil, W5DXP wrote:
"Here`s a quote from "Optics" by Hecht:
"Because bith phasors rotate together at a rate w, we can simply freeze
them at t=0 and not worry about their time dependence, which makes them
a lot easier to draw."

Raymond B. Yarbrough writes in the 5th ed. of "Electrical Engineering
Reference Manual" on page 1-1:
"A complex number can also be represented as a two-dimensional vector
in a complex plane. Thus, the complex number can be written in polar or
phasor form as

a+jb=c on an angle phi

c=square root of a squared + b squared

phi = arctan (b/a) "

On page 3-15 Yarborugh wrote:
In electric circuits involving sinusoids it is more convenient to deal
with RMS values of voltage and current rather than with peak values, and
with angles in degrees rather than with radians (Angles in the
exponential form must be in radians for mathematical calculations.)

Thus, an alternative representation, which is called the effective value
phasor notation has evolved."

Best regards, Richard Harrison, KB5WZI