CONCEPTUAL TOOLS	By:  Carl H. Durney and Neil E. Cotter	Phasors
		Phasor<->inverse-phasor
		Example 2

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Ex:            If  find , (i.e., find the inverse phasor)

Ans:

Sol'n:        We convert to polar form:

                  Now use the standard inverse phasor identity:

                  Note:    There is no math to do here—we just substitute the values of A and  into the cos( ).

                  Note:    We don't know the value of  for this problem.  Thus, we just use a symbolic variable for .  The value of  is not part of a phasor.  (The value of  must be kept track of separately.)

                  Using the identity gives the answer:

Note:        Mathematically, it is also correct to invert the given phasor in two pieces, with the real part giving a cosine term having no phase shift and the imaginary part giving a (negative) sine term having no phase shift:

.

                  Although this answer is correct, it is usually easier to visualize a single sinusoid with a phase shift.  The sum of the cos and sin terms is equal to the single cos with a phase shift given above.  This follows from the observation that the sum of any number of sinusoids of the same frequency may be expressed as a single sinusoid of that frequency.  (The challenging part is determining the magnitude and phase shift of the single sinusoid.)