A Complement to Compliment
Recently when writing a quick note I used the phrase “with complements of.” Only upon re-reading my note (after I sent it) did I realize it should have been “with compliments of.” Curious about this distinction, which I hadn’t even consciously realized existed, I turned to the ultimate authority for clarification.
Evidently the word was originally spelled “complement,” having derived from Latin through French. Sometime between 1650 and 1725, however, the French word “compliment” supplanted the second definition of “complement.” Thus, by the mid 1700s English had developed two different words:
Complement: that which completes or makes perfect
Compliment: polite expression of praise or flatter
Of course those are only two of several definitions of each, which both have noun and verb forms, but they are relatively representative on the whole. Upon inspection, it does seem clear that having two different words is useful here. But that doesn’t change the fact that the French “compliment” staged a hostile takeover of the English language.

Interestingly, the title could also be “A Compliment to Complement” and it would also make sense.