How does a bandpass filter work?
You're wanting the magnitude of your spectrum to decrease in certain areas (since you're trying to filter out those frequencies). So, yes, you could just multiply your real and imaginary components by your coefficient. For example, if you have a number $5 -5i$, the magnitude is $\sqrt{5^2 + (-5)^2} = 5\sqrt{2}$. If you want to decrease this magnitude by 50% you would just multiply your real and imaginary numbers by .5. This can be seen by $\sqrt{(5*.5)^2 + (-5*.5)^2} = 2.5\sqrt{2}$.
Note that if you're wanting to filter your signal in the frequency domain, and then transform it back to the time domain, you probably don't want to do a rectangular window, where you multiply the frequencies you want to filter out by 0, and everything else by 1. This would create some wide band noise in the time domain.