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The use of complex quantities in the theory of alternating currents was pioneered by Charles Proteus Steinmetz in his work, Alternating Current Phenomena. Early writers used complex quantities to represent vector quantities algebraically. Steinmetz extended the application so as to include harmonic quantities. As many writers in electrical engineering are prone to confuse vector and harmonic quantities, the author thinks it is necessary to distinguish these two uses of complex quantities, and for that purpose he starts with the vector use and later takes up the harmonic use. In many...