Does the complementary color always work as a CTA?
Only if its lightness differs enough from the surrounding background. The 180-degree relationship guarantees hue contrast, the perceptible gap between tones, but two complementary colors can share similar lightness and still blend visually on a neutral background; adjust the CTA lightness (L) beyond what hue alone provides.
Why does the palette return five colors instead of just two?
Because a real button needs more than one visual state: resting color, hover, focus and maybe a highlight badge. The three extra colors sit 150, 210 and 30 degrees from the base, close enough to the pure complement to stay in the same hue family without repeating the exact HEX for every state.
Do I still need to check contrast when already using a complementary color?
Yes. Hue harmony measures distance on the 360-degree circle, reading contrast measures the luminance ratio between text and background. They are different mathematical axes: WCAG 2.1 requires 4.5:1 for normal text and only accepts 3:1 from large text upward (24px regular or roughly 18.66px bold), and neither number comes from the hue angle.
How do I choose between the pure complement and a 150 or 210 degree neighbor?
Reserve the pure complement (180 degrees) for the resting state, the one seen the most, and use the 150 and 210 degree neighbors for hover and focus: the 30-degree gap between them is perceptible enough to signal a state change without reading as a different brand color.