What are complimentary colors?

Answer 1

either colors you get for free
or complementary colors with a spelling mistake
Two complementary colors mixed will give white or black (depending if you use additive or subtractive color mixing) that is they complement each other. Nothing at all to do with compliments.
Look up definition for complementary colors on wikipedia, it's pretty good.

Answer 2

Complimentary Colors: "Red and Green, Blue and Orange, Purple and Yellow. These are the colors directly across from eachother on the color wheel. Don't let the name fool you, they rarely look good when used together. They're called "complimentary" because, when used together, they become extremely vibrant and have heavy contrast. Complimentary colors are useful when you want to make something stand out. For example, if you use a green background and have a red circle on it, the red will jump off the page and be almost blinding." Source: http://www.liquisoft.com/colortheory.html

Answer 3

Opposite colors on the colors wheel.

Try finding an object in the room that brightly emanates some color. Put a blank white piece of paper next to it. Stare at the object for at least 30 seconds then quickly move your eyes to the blank sheet. The color you see is it's complementary color.

This is why when you stare at the sun's orange/red glow you will often see a blue/green spot when you look away.