Complex impedance

Impedance is resistance's richer cousin for AC circuits: it measures not just how much a component opposes current, but also how much it shifts the current's timing relative to the voltage. Written as a complex number Z = R + jX, its real part R is ordinary resistance (which burns energy), and its imaginary part X — the reactance — captures the energy-storing, phase-shifting behavior of capacitors and inductors.

An ideal resistor has Z = R with no phase shift; an inductor has Z = jωL, so its opposition grows with frequency and it makes current lag voltage by 90°; a capacitor has Z = 1/(jωC), so its opposition shrinks with frequency and current leads voltage by 90°. With impedances in hand, Ohm's law generalizes beautifully to V = I·Z, and series/parallel combination rules carry straight over from resistors — letting you analyze filters, resonant circuits, and matching networks with the same algebra you already know.