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1.
A man's stubbornness to ask for directions, even when he has no idea where he is.

Derives from the story of Christopher Columbus, whose wife would nag in his ear for him to ask for the quickest way to India.
Woman: We've passed that gas station twice already. Overcome your Columbus Complex and ask for directions.
Man: No, I know exactly where we are.
by thebetterfriend2 September 28, 2010
 
2.
The feeling of entitlement to an area even though you weren't here first.
"I was here studying first when a group of kids with Columbus Complexes came in & looked at me like I should leave"

"I was using this machine at the gym when a guy with Columbus Complex swooped in & used it without asking if I was done"
by viv0vivi March 13, 2014