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

I have recently started to learn about Complex Number's applications in AC circuits and its advantage over Phasor methods.

What I want to know is that suppose I am given with 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.

Please forgive the question to be too obvious as I am from a Physics and not Electrical Engineering background.