Q:

What part does 「成」 play when tailed to a word?

So I recently came across a song called 「未完成」 by Leo Ieiri.
I know 未完 means "Incomplete" or "Unfinished". I'm interested in knowing what that 「成」 represents when used after 「未完」 and what are other ways to use it.

A:

I think you're parsing it incorrectly... It's 未+完成, not 未完+成.
[未]{み} - prefix, "not yet" "un-"
[完成]{かんせい} - "completion" "accomplishment" "perfection" 

