reactive components are modeled as imaginary numbers
Reactive components are analyzed via differential equations. The imaginary/complex number (and/or phasors) is a mathematical simplification for the case of sinusoidal signals (ie all interesting signals) because cos(wt+p) = Real(ei*(wt+p)), and exponential functions have lovely properties when it comes to doing calculus on them. And i has lovely properties in power series. (i2 = -1, i3 = -i, i4 = 1, i5 = i, etc.) So by using complex numbers, the actual math gets much easier.
But in the end, reactance is just like resistance, except that there's a frequency dependence, and a change of phase in the result.