given the time-domain voltage v=4cos?(πt/6) V, find the average power that result when the corresponding phasor voltage V=4∠0° V is applied across impedance Z= 2∠60° Ω.

My question is : As average power is present only inthe resistive component, so I need to calculate for Re|Z|=1 Ω and Veff=2√2 rms. and then the average power P= 8 watt(using P=Veff^2/R)

but as solved in the example , V/Z=2∠-60° A and P= 1/2(4)(2) cos 60°= 2 watt.

what's wrong with the first method?