If you stare fixedly at a bright light and then close yours eyes,
you’ll see an afterimage in the complementary colour
(provided you don’t have a colour vision deficiency).
This could be used as a definition of
because the meaning depends on a viewer’s perception—it doesn’t depend
on the technicalities of computer displays or the technicalities of mixing oil paints.
Unfortunately, this definition would be quite impractical.
Two colours are complementary if they produce a mid grey when they’re mixed in equal quantities. The proper mixing can be achieved by applying each colour to half a circular disc, then spinning the disc very rapidly. In this way the mixing occurs in the human eye. Another valid method of mixing the colours is to make a fine grid in which the colours alternate. Mixing the colours on a paint palette is not a useful guide because all the strange variations and the diversity of pigment technologies have nothing to do with a viewer’s perception of the original colours.
Look closely at the central square in the illustration on this webpage; the computer has been instructed to draw a very fine check pattern—a finer version of the other patterns. Stand back enough and your eye will blend the dots into a uniform square. If this square is a mid grey like the background on these webpages, then the two colours are complementary (or approximately so, depending on the accuracy of the adjustments of your computer monitor).
Don’t stare at the illustration for too long or the afterimages of the squares will start to affect your perception of the colours. This is what can happens when you stare at a pointillist painting or a work of op art.