The difference between impedance and resistance

One way of dealing with any signal is via Fourier analysis. That analysis, along with a host of other signal analysis techniques, benefit greatly from Euler's identity, without which the analysis would be unnecessarily cumbersome. There is simply no good reason to express signals in any other way when engaged in any such analysis.

Bob: It goes back to basic em fields. As to inductance the motion of a charge (which is current) causes a magnetic field. If the current is varying with time the magnetic field will vary wtih time. A time varying magnetic field causes a voltage in any conductor that is linked by that field. "Inductance" is by definition the circuit paramater that relates the voltage just described with the current that caused the voltage. There is a somewhat analogous explanation for capacitance, with the difference being that field is not a magnetic field but rather an electric field, the cause of which is a separation of charge. Remember that a "circuit" can consist of a wire. We construct specific elements to control the relationship which is inductance or capacitance.

Bob: While reading the links keep in mind that the 'phase' difference is a way of describing the special case of the transfer function for a system when the input a sine wave and where the transients have died out (steady state).