Editing Electrical impedance (section)

=== Relation to phasors ===
In the [[phasor]] regime (steady state, meaning all signals are represented mathematically as simple [[complex exponential]]s <math>v(t) = \hat V\, e^{j\omega t}</math> and <math>i(t) = \hat I\, e^{j\omega t}</math> oscillating at a common frequency <math>\omega</math>), impedance can simply be calculated as the voltage-to-current ratio, in which the common time-dependent factor cancels out:

:<math>Z(\omega) = \frac{v(t)}{i(t)} = \frac{\hat V\, e^{j\omega t}}{\hat I\, e^{j\omega t}} = \frac{\hat V}{\hat I} \qquad \text{(phasor-regime impedance)}</math>

The phasor domain is sometimes dubbed the frequency domain, although it lacks one of the dimensions of the Laplace parameter.<ref>{{Cite book | last = Alexander | first = Charles | last2 = Sadiku | first2 = Matthew | title = Fundamentals of Electric Circuits | publisher = McGraw-Hill | year = 2006 | edition = 3, revised | pages =387–389 | isbn = 978-0-07-330115-0 }}</ref> For steady-state, the [[Complex number#Notation of the polar form|polar form]] of the complex impedance relates the amplitude and phase of the voltage and current. In particular:
* The magnitude of the complex impedance is the ratio of the voltage amplitude to the current amplitude;
* The phase of the complex impedance is the [[phase shift]] by which the current lags the voltage.
These two relationships hold even after taking the real part of the complex exponentials (see [[phasor]]s), which is the part of the signal one actually measures in real-life circuits.