I'm surprised - usually it's more difficult to get correct colors when using pigments. On the computer, colors are perfect. Blue and yellow always make green. Pigments are a lot more wonky. Haven't you ever encountered a blue and a yellow pigment that don't make green?
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Digital painting involves mixing light elements, which is different than the way that pigments mix together, especially with color complements. Do some seaches here or elsewhere on color theory and light, and that should start to clear things up for you.
When you're painting traditional, you just kinda arbitrarily mix the complementary colors on the canvas to get the right grey/shadow.
If your process consists of "arbitrarily mixing" until you happen to stumble upon the right color, no wonder you're having problems. That's no way to go about things, no matter what medium you're using.
1.Compared to those for paint mixing, the complementary relationships for digital colour mixing are DIFFERENT (as dbclemons says) and are much more precisely PREDICTABLE, as Seedling says, although the example she gives could be confusing (see 2 below).
2. Whether you are using Photoshop or Painter, the opposite colour you see on the colour wheel in the program shows you the exact complementary you need. Note in particular that pure blue (R=000 G=000 B=255), NOT purple, is the exact complement of pure yellow (R=255 G=255 B=000), as you can in fact see by the numbers in brackets.
3. To get the exact digital complement of any colour, use the colour picker to find out the value of the hue (H): the pure complement will be the pure colour with the exact opposite hue i.e. H+180, S=100 B=100 in Photoshop, or H+50% S=100% V=50% in Painter. Try it!
Another trick in Painter or PShop is to draw a color on one layer, make a new layer and draw over the bottom color with white, and then change the top layer method to "difference." That will show you the opposite hue.
you could also download a color wheel jpeg from the www and color pick to make color mixing feel more traditional. its kinda fun...sometimes. but the best part is never wasting pigment when you come up with mud.