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1.
To go well with; to complete.
That lamp complements your desk perfectly.
by Diggity Monkeez March 03, 2005
 
2.
In Math, the complement is, simply put, that which is outside of the defined region. However, this is often used as an insult in geek circles.

Geek 1:Your momma's so fat, that she's the complement of your house.

Geek 2: Yeah, well at least my penis isn't always the complement of a vagina.

Geek 1: *shoots self, thus becoming the complement of existing*
by Evariste Galois April 20, 2009
 
3.
Complementary compliments
So amazing how your complements go with the dinner service, dahling.
by Hercolena Oliver April 20, 2009
 
4.
something you give to someone you like
something you add to food to improve its taste
She accepted the complement with good grace
by Philip Nash November 26, 2006