I think "complete" is a problematic definition, but I think I know what you're aiming for (see my definition on the bottom).
Let's open with an easy example - looking at cars, what's a complete user interface?
- A wheel for steering
- Gas/break pedals (and hand break)
- Gear transition (automatic or shift)
- Lights, whippers, etc.
How about a radio/CD player? Is the car interface incomplete without it?
Strictly speaking - no! It's not a vital functionality for driving, but still most people would never consider having a car without a radio (unless it's a racing car, for example).
What about a cold drink fridge?
Most people would not think a car would normally have one... but what if the car is in fact a limo? Then without a fridge it wouldn't really be a limo now, would it?!
My point - "complete" refers to the needs and expectations of your target users.
So one of the key things you should do is approach your potential users and ask them:
"Hey, I've created a project-management/accounting/design/CRM/etc. application, what would you want it to enable you to do? What are the key features in your eyes? If it lacks ____ would you still consider it?"
One you have all the scenarios and features implemented, you do your regular usability testing to see if the users can accomplish all the things you've implemented for them (based on their requests and expectations).