complement (n.)
late 14c., "that which completes," from Old French compliement "accomplishment, fulfillment" (14c., Modern French complément), from Latin complementum "that which fills up or completes," from complere "fill up" (see complete (adj.)). Originally also having senses which were taken up c.1650-1725 by compliment.
complement (v.)
1610s, "exchange courtesies," from complement (n.). Meaning "make complete" is from 1640s. Related: Complemented; complementing.