What's the minimum number of genes needed to code for this complex?

Yes, you're right. There would be at least three genes; one encoding each of the polypeptides.

Your inference is most likely correct, in that there would be 3 different genes--one for each polypeptide.

Nevertheless, research conducted in past 10-15 years or so would state otherwise.  It is now known that many genes can produce multiple different proteins, or polypeptides, through various mechanisms.

If this question is for high school coursework or very elementary college biology, then the answer would be 3.  However, if you were to submit the answer "1" in one of my classes, I would certainly give you bonus points due to the fact that the "one gene-one protein" theory no longer holds true.