# Calculating reactive power given u(t) and i(t)

I would like to calculate the reactive power of a given two-pole which has the following voltage and current characteristic.

$$\u(t) = 2+5sin(\omega t)+2sin(2\omega t+\frac{\pi}{6});i(t) = 10+3cos(\omega t-\frac{\pi}{6})+8sin(3\omega t)\$$

So I know the reactive power is calculated by one the following formulas:

I started to work with phasors , I converted all the sin() functions into cos() like

$$\2sin(2\omega t+\frac{\pi}{6}) = 2cos(\frac{\pi}{2}-(2\omega t+\frac{\pi}{6})) = 2cos(\frac{\pi}{3}-2\omega t) \$$ then complex phasor $$\e^{j(\frac{\pi}{3}-2\omega t)}\$$ so i this this procedure for every trigonometric function in $$\ u(t) \$$ and $$\i(t)\$$

then i used the following formula:

and then simplified the whole expression, i hoped that the exponents will turn out to be the same but they differ.

This question is a small part of an signals and systems exam it's going for 2 points out of 30 so i am guessing (since my calculation taking so long) there is a faster and simplier way to get the right answer ? The following picture is just showing that all the exponents are different: