Kenneth G. Wilson (1923). The Columbia Guide to Standard American English. 1993.
supplement, complement (nn., vv.)
When you supplement something, you add to it: Well supplement our rations with what we can scrounge. When you complement something, you complete it, fill it out: His powerful ground game complemented her excellent volleying and net play. A supplement is something added: The new book was a supplement to the old. A complement is something that fills out or completes, as in Her recent essay complements the contributions of her predecessors; The arrival of the new recruits gave us a full complement of troops. See also COMPLEMENT.