This is a really good question! If you want to understand complementary colors, the first thing you need to understand is the ways that colors mix together. The hard part is that there are actually two different kinds of colors. The first is colors that work like paints (scientists call them "pigments"). You probably learned about these in your art class at school. The other kind of colors is colors of light.
For paint, the primary colors are red, blue, and yellow. (Primary colors are colors that you can mix together to make any other colors.) For this kind of colors, the complementary color is what you get when you mix the other two together. (For example, the complementary color of red paint is what you get when you mix blue paint with yellow paint - green paint.)
For light, the primary colors are red, blue, and green. By mixing these together, you can make any other color of light. These work the same way as colors of paint in that you can get the complementary color by mixing the other two together. Except that colors of light mix together differently than colors of paint do! Red and blue make magenta (bright pink), blue and green make cyan (blue-green), and green and red make yellow. So the color wheel for light looks a bit different than the one you're probably used to:
To get brown light, you have to mix lots of red with a little bit of blue and green. So to figure out what the complementary color is, you have to figure out what the complementary colors of all the parts are, and then mix them together. So you’d have to mix together lots of cyan with a little bit of yellow and a little bit of magenta. It’s sort of hard to imagine how that would work, but it turns out that when you mix those colors together, you just get cyan. So the complementary color for brown light is cyan (blue-green).
To figure out the complementary color for black, you have to understand a couple other things. The first thing is that with light, if you mix all the primary colors together (red, green, and blue) in the same amounts, you get white. (That’s why if you shine a white light through a prism, you get a rainbow.) If you mix any two complementary colors together, you get white, too. So if you mix blue light with yellow light, for example, you’d get white light (like the light in light bulbs). On the other hand, if you have no colors at all, you get black. So the complementary color for black light is white light (because if you add all the colors to no colors, you get all the colors).
(republished on 07/27/06)