Impedance of Inductive Reactance

It was learned in the chapter "Inductor" that for the pure inductor of [Fig. 1], the voltage leads the current by $90^\circ$ and that the reactance of the coil $X_L$ is determined by $wL$. By Ohm's law, Since v leads i by $90^\circ$, i must have an angle of $90^\circ$ associated with it.
To satisfy this condition, $\theta_L$ must equal $+90^\circ$. Substituting $\theta_L = 90^\circ$, we obtain so that in the time domain, The fact that $\theta_L = 90^\circ$ will now be employed in the following polar format for inductive reactance to ensure the proper phase relationship between the voltage and current of an inductor. The boldface roman quantity $Z_L$, having both magnitude and an associated angle, is referred to as the impedance of an inductive element. It is measured in ohms and is a measure of how much the inductive element will "control or impede" the level of current through the network (always keep in mind that inductive elements are storage devices and do not dissipate like resistors). The above format, like that defined for the resistive element, will prove to be a useful "tool" in the analysis of ac networks. Again, be aware that $Z_L$ is not a phasor quantity, for the same reasons indicated for a resistive element.