ABSTRACT An identity for a quadratic rational function is here applied to lumped-element linear electric circuits, where expressions involving such functions abound. These include the absolute values of impedances, expressions for the phase angle, natural frequencies of free oscillations, resonance and anti-resonance frequencies and characteristic impedances of wave filters. The arguments of these functions are the elements R, L, C and M, and the result of applying the identity to such functions is that one may replace these elements by other elements of the same kind but having different magnitudes, while the relevant functions remain invariant. For instance, positive elements may replace, in a two-terminal network, fictitious elements with negative, zero or infinite magnitudes, while the absolute value of the impedance remains invariant. In anti-resonant circuits, elements may be replaced by others, thus changing the impedance at anti-resonance, while the anti-resonance frequency is unchanged. In this p...