Give one of them the job
Two complements at equal area and equal saturation compete, and the eye cannot settle on either. Let one carry the design and keep the other for the thing you want clicked. The pair is a contrast device rather than a split.
A complementary color is the one directly opposite another on the color wheel, 180 degrees round. Side by side, each makes the other look more vivid. Mixed together, they cancel toward gray. On a screen the complement of red is cyan, which is not the green most people were taught, and the reason for that difference is worth two minutes.
Two colors from opposite sides of the wheel. They make each other look more vivid, which is why the pairing is used for anything that needs to stand out.
Drag the wheel or use the arrow keys on the marked handle. Hue 251°.
Computed by rotating the hue 180 degrees, the same calculation behind the wheel above and the schemes on all 131 color pages. Click a code to copy it.
Both answers are right, for different color models. Paint mixes pigment and subtracts light, on the red-yellow-blue wheel that predates anyone mixing light at all. A screen adds light, on the red-green-blue wheel. Same word, different geometry, different opposite.
Art teaching says green. Your screen gives #00FFFF, because that is the value that cancels red back to white when the two are added as light.
Art teaching says orange. Your screen gives #FFFF00, because that is the value that cancels blue back to white when the two are added as light.
Art teaching says purple. Your screen gives #0000FF, because that is the value that cancels yellow back to white when the two are added as light.
Neither model is a better description of color. They answer different questions, and the one that applies is whichever medium you are working in. For anything that will be looked at on a display, that is RGB.
Two complements at equal area and equal saturation compete, and the eye cannot settle on either. Let one carry the design and keep the other for the thing you want clicked. The pair is a contrast device rather than a split.
Most complementary pairs that work in practice are not both at full strength. Muting one keeps the hue relationship, which is what gives the vividness, while removing the fight. The shade and tint ramps on any color page are the quickest way to find that version.
Saturated complements meeting along a border can appear to shimmer, an artefact of how the eye handles equal-brightness edges. A neutral between them, or a difference in lightness, removes it. This is also why complementary text on a complementary background usually fails contrast even when it looks striking.