Complication and compilation are easily confused words.
The spell-check application of most word processing software programs would not catch a slip-up of these two words. Spell-check is looking for words that aren’t in its dictionary, and words that resemble words in its dictionary but are possibly spelled wrong. Spell-check isn’t perfect. It doesn’t know and can’t guess what word you wanted or what word you meant, it can only judge the words on the page. If you used words that are all spelled correctly, it gives you a pass anyway.
Autocorrect suggests words that start with the same letters. It suggests what word you may want to save time, but quite often, its suggestions couldn’t be more off base and produces humorous results.
Complication is a noun. It means a problem or a difficulty that happens, or could potentially happen in a planned course of action.
Compilation is a noun, it’s related to the verb compile. It means a grouping or a collection of things.
The following story uses both words correctly:
Connor wanted to record a compilation of his favorite songs, the ones that inspired him to become a musician. He found lots of complications with obtaining the licensing for some tracks.