Complex impedance magnitude and phase applies to one frequency.

Complex impedance Z = R + j X = |Z| (cos θ + j sin θ) = |Z| ejθ = |Z|∠θ

Impedance magnitude |Z| = √(R2 + X2)

Phase angle θ = arctan (X / R)

Resistance R = |Z| cos θ     Reactance X = |Z| sin θ

Inductance L in Henries     Capacitance C in farads

jXL = jωL      jXC = 1 / jωC = -j / ωC

Inductive Reactance XL = ωL     Capacitive Reactance XC = -1 / ωC

Reactance X = XL + XC = ωL - 1 / ωC

Angular frequency ω = 2πf

Audiophile Heretic, June 24, 2026