In this problem we are being asked to find the value of the inductance L if the impedance of the net work is real at 60 Hz.
In this context, the term "real" means that the impedance of the circuit has no imaginary part. The term “real” indicates that the reactive impedance is at 0° and can be replaced by a short circuit. Let's look at this in terms of the impedance equation…
Z = 1 Ω and 2 Ω in parallel with the impedances of the inductor and the impedances of the capacitor which is zero… therefore, the reactance impedances must cancel each other, providing zero impedance… or a short circuit around the 2 Ω resistor… that means the term 2||[XL + XC] must be “0” … that can only happen when the term