The electric conductivity and magnetic conductivity parameters represent the material losses. In frequency-domain simulations under a time-harmonic (e<sup>jωt</sup>) field assumption, it is often convenient to define a complex relative permittivity and a complex relative permeability in the following manner:
:<math> \epsilon_r = \epsilon^{\prime}_r -j\epsilon^{\prime\prime}_r = \epsilon^{\prime}_r -j\frac{\sigma}{\omega \epsilon_0} = \epsilon^{\prime}_r (1 - j \tan \delta ) </math>
:<math> \mu_r = \mu^{\prime}_r -j\mu^{\prime\prime}_r = \mu^{\prime}_r - j\frac{\sigma_m}{\omega \mu_0}= \mu^{\prime}_r (1 - j \tan \delta_m)</math>
where ω = 2πf, and f is the operational frequency. It is also customary to define , and the electric and magnetic loss tangents are defined as follows:
:<math> \tan \delta = \epsilon^{\prime\prime}_r / \epsilon^{\prime}_r </math>
:<math> \tan \delta_m = \mu^{\prime\prime}_r / \mu^{\prime}_r </math>
Three special media are frequently encountered in electromagnetic problems are:
* '''Vacuum''' or '''Free Space''': ε<sub>r</sub> = μ<sub>r</sub> = 1 and σ = σ<sub>m</sub> = 0