Sounds like you have confusion regarding "Impedance" and "Reactance" (judging by the following statement "...Impedance of inductor and capacitor when circuit oscillate should be equal"). The Reactance of the inductor and the capacitor, at resonate frequency, is equal in magnitude. The impedance is purely resistive because the inductive reactance and the capacitive reactance have a 180 degree phase difference, thus they cancel, leaving only the resistive component.
Reactance is the AC resistance of either a capacitor or an inductor. Impedance is the vector sum of Capacitive Reactance, Inductive Reactance and DC Resistance. _Impedance_ is not the same thing as _Reactance_. They can have the same value, in cases where there is only resistance or only capacitance or only inductance in a circuit (or device), but ONLY in those cases (and, technically, there is no such circuit). And, having the same value, doesn't make then conceptually the same. It's very important for you to learn this distinction (or change this habit of referring to _reactance_ as _impedance_).
