Compliment vs Complement - Common Mistakes in Usage

These are sources from Wikipedia :

http://en.wikipedia.org/wiki/Compliment

Compliment may be

• An expression of praise, congratulation or encouragement.
• The correct respectful actions paid to a superior, such as saluting an officer in the armed forces.

http://en.wikipedia.org/wiki/Complement

In many different fields, the complement of X is something that together with X makes a complete whole—something that supplies what X lacks.