What is complex power and how is it calculated in AC circuits?

Complex power S combines real and reactive power in a single complex quantity: S = P + jQ = VI* (where I* is complex conjugate of current). In rectangular form, S = VI(cos(phi) + jsin(phi)). Magnitude |S| is apparent power, real part is real power P, imaginary part is reactive power Q. Complex power simplifies AC power calculations and provides complete power flow information including direction and power factor.