What's particularly useful is that Ohm's law holds with complex numbers. If one has a linear circuit (a circuit consisting of nothing but resistors, caps, inductors, and 'perfect' amplifiers) and wishes to see how it will behave when driven at a particular frequency, after computing the reactances of all the caps and inductors at that frequency one can easily figure the voltage at any point in the circuit or current through any wire. If a voltage is, e.g., 3+(3i) volts, that means that there will be a sine wave there with an amplitude of about 4.2 [sqrt(3^2+3^2)] volts, whose phase leads that of the driving signal by 45 degrees.