I am a physics undergrad, looking for ways to solve complex circuits efficiently.

I have recently started to learn about complex number applications  in AC circuits and its advantage over phasor methods.

What I want to know is that suppose I am given a complex AC circuit and I am required to find its impedance and phase factors. Can I do this by imagining the AC circuit to be a DC circuit at every instant, treating capacitors and inductors as if they were resistors and following the parallel/series combination methods of resistance addition? 

Note: I am mainly interested in sinusoidally varying voltage sources and resistors, capacitors and inductors.

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Please forgive the question to be too obvious as I am from a physics and not electrical engineering background.