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COMPLEMENT/COMPLIMENT |

Originally these two spellings were used interchangeably, but they have
come to be distinguished from each other in modern times. Most of the
time the word people intend is “compliment": nice things said about
someone ("She paid me the compliment of admiring the way I shined my
shoes”). “Complement,” much less common, has a number of meanings
associated with matching or completing. Complements supplement each
other, each adding something the others lack, so we can say that
“Alice’s love for entertaining and Mike’s love for washing dishes
complement each other.” Remember, if you’re not making nice to someone,
the word is “complement.”
A complement can also be the full number of something needed to make it complete: “my computer has a full complement of video-editing programs.” If it is preceded by “full” the word you want is almost certainly “complement.”
See also complementary/complimentary