In thinking of an inductor as a circuit element, it is to consider its limiting behavior at high and low frequencies. at one extreme, the inductor might behave like a short circuit, that is, like a resistor with almost no resistance (an ideal wire) having essentially no voltage drop across it no matter what the current. alternatively, the inductor might behave like an open circuit, that is, like a resistor with large resistance so that essentially no current will flow no matter what the applied voltage. based on the formula you obtained for the reactance, how does an inductor behave at high and low frequencies?

An inductor is just a coil of wire with magnetic properties. It is a device that stores electromotive force or energy in the form of magnetic field.  A current yields a magnetic field around it through a conductor. The pattern of flux for this magnetic field would be the number of concentric circle perpendicular to the detection of current. The capacity of the inductor is affected by the number of coils which would give more inductance, the material that is used for the coil, the cross sectional area of the coil and the length of the coil. For instance you have an 8 meters diameter coil with seven loops of wire. You place the coil on an area where there is a parked car. The inductance of the coil will be much larger compared to the coil without a parked car nearby because of the presence of the steel from the car. It changes the magnetic field of the coil because it acts as a core of the inductor.

they should be similar or the same