What is a complete subject?

Answer 1

A complete subject is the simple subject plus the words that modify it.

Example: The boy with blue hair is a math genius.

Simple subject: boy
Complete subject: The boy with blue hair

Example:
One of my best friends is going to Vietnam this summer.

Simple subject: One
Complete subject: One of my best friends

Check this site.

http://ace.acadiau.ca/english/grammar/gsubpred.htm