Power of a component in an AC circuit
If you know the voltage at the node, you could use a voltage divider to find the voltage across the resistor and get the power that way.  You can also calculate the complex power using the voltage at the node and the current through the series 2 Ohm resistor and capacitor branch.  The real part of the complex power is the average power, which is what is absorbed by the resistor.  Both calculations should give the same result.  Unless told otherwise, the voltages and currents in the circuit are going to be peak values at some phase angle that will come out of the analysis.  You will need to divide the current and voltage by the square root of two to get the RMS power in the resistor.