The scarf is a perfect complement to her outfit.
This pattern is easy to understand,
A is complement to B
The green wallpaper is the perfect complement to the old pine of the dresser.
Again, the same pattern
A is complement to B.
To make it easier to understand, could I say "B was missing something, A could help"?
The completeness is more about beauty, in particular, some kind of addition to existing beauty.
However, that kind of completeness is probably difficult for someone, like me, to understand. I'd never managed to distinguish my wife's scarves. So, I can't even make up what B is missing in any of those examples!
Besides, beauty is somehow a matter of opinion. Are there some other situations where the complement is easier to measure?
For example, could I call my headset a complement to my laptop, which can let me hear whatever I want to listen to without disturbing anyone else?
We had a full complement of reporters and photographers along.
This example doesn't use the pattern
A is complement to B, which makes it difficult to say B is missing what.