If instantanoeus power is p(t) and instantaneous voltage and current saying for a resistor are v(t) and i(t), then p(t)=i(t)*v(t). But if you convert v(t) and i(t) to their respective phasors and multiply them, the product is NOT the phasor of p(t).
For example, for R=3 Ohms,$$v(t)=6*cos(120\pi+30^{\circ})$$ and $$i(t)=2*cos(120\pi+30^{\circ})$$. Therefore, $$p(t)=12*cos^2(120\pi+30^{\circ})$$, or $$p(t)=6(1+cos(240\pi+60^{\circ}))$$.
The problem is if I try to multiply $$V=6\angle{30^{\circ}}$$, which is the phasor of v(t), by $$I=2\angle{30^{\circ}}$$, the phasor of i(t). The resulting product $$P=12\angle{60^{\circ}}$$ is equivalent to $$p_1(t)=12cos(120\pi+60^{\circ})$$.
p1(t) is not equal to p(t). What did I do wrong?