In modern color theory, complementary colors indicates those colors that are opposite each other on a color wheel. The color wheel is a wheel of red, blue, and yellow split into three equals sections. From there, six sections are formed with the three being mixtures of two of each primary color. Split those again and mix the adjoining two to form the wheel. Yellow is complementary to a few hues.
Directly across from yellow on the color wheel is purple. Very saturated complimentary colors can appear jarring, so watch the color scheme closely. Famous examples of this pairing include traditional Easter colors and the Los Angeles Lakers basketball team. On a black background, these colors are even more vibrant. On a white background, these colors appear less evocative, but still complementary. Strict complements are usually found in nature, usually with one color being dominant.
Triad complements are found when the base color is paired with two other colors evenly spaced on the color wheel. In the case of yellow, the other two evenly spaced colors are the remaining primary colors. Yellow, red and blue all are complementary to each other, when the three are used. This complement case is always especially vibrant, so use one base to dominate the picture and the other two sparingly for accents.
Split compliments are found when the base color has two off-complements of the initial complimenting color. For yellow, the complement is purple, so the split compliments would be red-purple and blue-purple. This complement scheme is a bit less vivid than strict complements, but still achieves a strong sense of cohesive unity and hue balance. Split compliments work, according to Tiger Color, because "this color scheme has the same strong visual contrast as the complementary color scheme, but has less tension."
Tetradic complements are found when the base color takes three other colors in a rectangular shape along the color wheel. In the rectangle, two sides will have one color between the compliments, and two sides will have three colors in between the complements. For any base, two rectangle complements can be made. The first color scheme would be yellow, orange, purple, and blue. The second set would be yellow, green purple, and red. Note that purple appear in both.