John Milton and John Bunyan, standing at widely different angles of experience, make one of the most interesting complementary
pairs in all literature.
Robert Huntington Fletcher -- A History of English Literature
completing the whole or going well together
There are many specialized uses of complementary including:
complementary colors: when mixed together give white (in the case of lights) or gray (in the case of pigments)
complementary angles: together form a right angle (90 degrees)
complementary terms: forming the whole such as male and female
complementary genes: work together to have an effect
Do not confuse senses of complimentary with this word.