In the CMYK color space the Primary Colors are Cyan, Magenta and Yellow. Here are some numbers that represent the color RED . These are the CMYK equivalents of the RGB values for pure red . This will be helpful for understanding complementary colors. Complementary colors are mutually exclusive.
Pure red contains absolutely no cyan and vice versa.
Pure blue contains absolutely no yellow and vice versa. Pure green contains absolutely no magenta and vice versa. The fact that complementary colors sit opposite each other is because they are literally the opposite of each other. For instance, cyan pigments appear cyan precisely because they absorb red light and reflect blue and green. Cyan is the absense of red.