WordNet records no synonym and no antonym for complementarity. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a relation between two opposite states or principles that together exhaust the possibilities
the interrelation of reciprocity whereby one thing supplements or depends on the other
“the complementarity of the sexes”
Synonyms, antonyms and the broader and narrower relations for complementarity come from Princeton University’s WordNet. Full sources and licences.