Is it farther or further?
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.
1610s, "exchange courtesies," from complement (n.). Meaning "make complete" is from 1640s. Related: Complemented; complementing.
complement com·ple·ment (kŏm'plə-mənt)
A group of proteins found in normal blood serum and plasma that are activated sequentially in a cascadelike mechanism that allows them to combine with antibodies and destroy pathogenic bacteria and other foreign cells.