How to calculate inductive and capacitive reactance

So my question is does inductive motors

I think you mean induction motor.

Electric motors are energy conversion devices and an ideal electric motor converts 100% of the electrical power it receives from the circuit to mechanical power - the ideal motor itself does not consume power but, rather, changes its form.

Of course, for real motors, there are loses due to e.g., winding resistance, friction, etc.

Now an inductor and a capacitor are energy storage circuit elements - they alternately store and then release energy from and to the electric circuit to which they are attached.

So, for ideal inductors and capacitors, there is no loss - on average, their associated electric power is zero. The instantaneous power associated with an ideal reactive element is alternately positive and negative.

However, for a resistance, the electric power from the attached circuit is dissipated - converted to heat. The instantaneous power is always positive.

A definite mistake is your method of calculating total RMS voltage. In the absence of anything else other than "240V" and "21V", you have to assume these are RMS but you have assumed they are peak.

You could argue that you are right but not really, because you used them as RMS voltages earlier on to calculate currents and these will also be RMS values that you don't need to divide by sqrt(2) either.

Other than that and me not understanding the term "displacement power factor" and "true power factor" you are correct.