Etymology
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complementary (adj.)

1620s, "ceremonious" (a sense now obsolete in this spelling of the word), from complement (n.) + -ary. Sense of "forming a complement, mutually completing each other's deficiencies," is attested by 1794, in reference to the calendar of the French Revolution; in reference to colors which in combination produce white light, by 1814. Earlier in the sense "completing, forming a complement" was complemental (c. 1600).

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Definitions of complementary
1
complementary (adj.)
of words or propositions so related that each is the negation of the other;
`male' and `female' are complementary terms
complementary (adj.)
acting as or providing a complement (something that completes the whole);
Synonyms: complemental / completing
2
complementary (n.)
either one of two chromatic colors that when mixed together give white (in the case of lights) or grey (in the case of pigments);
Synonyms: complementary color
From wordnet.princeton.edu