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position at t = 0 is that of the complex phasor, and rotate it in a counter-clockwise

direction on the Argand diagram at an angular frequency w, starting at time t = 0 at the

position illustrated in Figurę 1.1, and watch the values of the projection on the horizontal

axis of the rotating arm which results.

Notice in the above exposition that we have not said that the phasorrotates. To do

so would contradict the definition of the phasor as a time invariant quantity. We have

given a different name, namely rotating arm, to the thing that rotates.

In establishing the notation described above, we have been able, because it is available,

to use different calligraphy, namely v (italic) and V (upright Roman), to distinguish the

real time-varying variables directly representing the physical quantities, and the time

invariant complex phasorsindirectly representing them. The difference in notationis

helpful in avoidingmisunderstandings.