Something's bugging me. Suppose we take kvl around a loop in a circuit, we have: v1(t)+v2(t)+....=0 Suppose v1, v2, v3(t) are all sinusoidal (they can be written as Acos(wt+s)). So we have A1cost(wt+s1)+A2cost(wt+s2)+....=0 Suppose we replace all of them by their phasors, this should also equal zero but why? I'll write it out here (without suppressing e^jwt, but just adding the imaginary parts) (A1cos(wt+s1)+A2cos(wt+s2)+....) + j(A1sin(wt+s1) + A2sin(wt+s2)+....) If I know the group of real terms add to zero, does that necessary imply that the group of imaginary terms add to zero? Is there a proof of this?