I guess this belong's in the abstract forums. But I am wondering what is the proof behind why kirchcoffs rules still apply to phasors. What I mean is once you convert the sine voltage/ current functions into phasors. Why does all the laws still hold with working with phasors? And why can you add phasors and translate back into a sine wave that would be equivalent to do the arithmetic with trig function identities always. I hope you don't miss understand this question. I know how to do the math but I don't fully understand the proof why the phasor kirchcoffs rules hold. I see no link between them. One is a number (phasor ) that represents trig function (sin wave voltage ac ...etc) The other is the actually equation for voltage , current etc etc... Note I am looking for proof. I can kind of see the translation between phasors to trig function and visa versa ( except it is not a one to one corospondences) Anyway I will stop rambling on. Thanks for any help.