Magnetic complex reluctance

Magnetic complex reluctance is a measurement of a passive magnetic circuit dependent on sinusoidal magnetomotive force and sinusoidal magnetic flux, and this is determined by deriving the ratio of their complex effective amplitudes.
As seen above, magnetic complex reluctance is a phasor represented as uppercase Z mu where:

and represent the magnetomotive force
and represent the magnetic flux
, lowercase z mu, is the real part of magnetic complex reluctance

The "lossless" magnetic reluctance, lowercase z mu, is equal to the absolute value of the magnetic complex reluctance. The argument distinguishing the "lossy" magnetic complex reluctance from the "lossless" magnetic reluctance is equal to the natural number raised to a power equal to:
Where:

is the imaginary number
is the phase of the magnetomotive force
is the phase of the magnetic flux
is the phase difference

The "lossy" magnetic complex reluctance represents a magnetic circuit element's resistance to not only magnetic flux but also to changes in magnetic flux. When applied to harmonic regimes, this formality is similar to Ohm's law in ideal AC circuits. In magnetic circuits, magnetic complex reluctance is equal to:
Where:

is the length of the circuit element
is the cross-section of the circuit element
is the complex magnetic permeability