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In this paper, a new mathematical method of electrical circuits calculus isproposed based on the theory of the complex linear operators in matrix form.The newly proposed method generalizes the theory of complex representation ofelectrical quantities in sinusoidal periodic regime to the non-sinusoidalperiodic regime.

The generalization of A. E. Kennelly theory of complex representation of  the electrical quantities in sinusoidal periodic regime to the one and  three-phase electric quantities in non-sinusoidal periodic regime