Compliment vs. Complement

Not long ago I was driving in my hometown of Sacramento, CA, and saw a building that advertised itself as a "center for complementary medicine". Looking at the businesses housed within the building, I thought that they had merely spelled the descriptor wrong (how embarrassing!). However, the error was mine. Curious to know if "complement" was such a word, I decided to look it up. Ta Da! There is such a word as "complement", although its meaning is similar to "compliment".

"Compliment" means to say something nice about someone (e.g. "I like your new haircut.").

"Complement" means that two or more things go together, or complete each other. In the case of the medical building in Sacramento, it housed massage therapy, acupuncture, holistic medicine, and other alternative medical businesses.