Another way of writing this, again, going back to the fact that we want a formula.

My output Amplitude.

My output amplitude is equal to my input amplitude,

times the magnitude of the transfer function.

My output phase, right there, is equal to the input phase,

plus the phase of the transfer function.

So, this right here, very important formula, because this allows us,

given a sinusoidal input.

To figure out what the sinusoidal output is, if I have that transfer function

as a characteristic way of representing the circuit.

Let me look at an example of an RC circuit.

I want to find the transfer function.

Ultimately, what I'd like to be able to do is solve for

V out, but the step along the way is to find that transfer function.