If someone at the office today says they like your Christmas tie, that’s a compliment. If you ask yourself why in the world your red and green tie could be worthy of a compliment…now that’s about complement.
A complement refers to making something whole or complete. It applies in geometry, music and art: a complementary angle completes another to make a 90 degree or right angle; a complementary interval in music completes an octave; a complementary color, when added to another, completes black on a color wheel (or white on a light spectrum). A complement of employees would be all those necessary to do a job; a compliment of employees would be… great job!
Complementary colors attract. They’re in maximum contrast , but also are in what is called “color harmony” in painting. Red and green (and other complements) are directly opposite on the color wheel. Side-by-side, they maximize contrast. (Traffic light engineers are no fools.) Red and green also harmonize. Things that make a whole when combined tend to attract visually.
So the tie might get a compliment if it’s a complement. (That won’t fix the giant Santa tie problem.)