My sense of the word complement is that if two things are complements, they sum to 1, or some equivalent.

A is the complement of ~A because P(A or ~A) = 1

Red and green are considered to be complementary colors because together they contain all primary colors of pigments. [although, that is based on the societal understanding that the primary colors are Red, Yellow and Blue. This is actually incorrect. For pigments, the primary colors are really Magenta, Yellow, and Cyan. For light, they are Red, Green, and Blue.]