Question

A , static character stays the same even though there is conflict in the story.

Answer 1

Answer;
A FLAT, static character stays the same even though there is conflict in the story.

Explanation; 
A static character is a character that stays the same through the story. 
A flat static character reveals only one or two personality traits that do not change. Unlike the Round characters who have a complex personality; and are often potrayed as conflicted and contradictory characters.

Answer 2

Correct, static characters usually don't change or change very little throughout the course of a narrative.