Definition: A complex character is a multidimensional character who changes their attitude to suit whatever environment they happen to be in.
Example: Beverly Goldberg, from ABC's The Goldberg's is a wonderful example.
Explanation: Beverly Goldberg plays the role of the often-overbearing mother who will do anything to make her kids happy and be their best friend. Throughout the course of the first season (the second season premiered (9/24/14). Beverly does things that are typical of the overbearing mother such as spying on her children, not allowing them to do certain things because she thinks it will hurt them, and putting rules and restrictions on her children that to some seem superfluous. She is also the type of mother who wants to be a best friend to her children. .
As a result, she will sometimes agree to things because she thinks it is what her children want, even if she does not personally agree with it, or she will try to show interest in something that her kids like just to get them to like her, which doesn't always go the way that she had planned for them to. Beverly is complex because she adapts to her changing environments so much that it is sometimes hard to get a grip of the kind of person she really is. The directors use Beverly Goldberg effectively as a character because, through her, they show the struggles of what real women go through as mothers and give them something that they can identify with.
Definition: A dynamic character is a character, often a major one, that changes significantly during the course of the story. It is often one of the major characters.
John Hickam from the movie October Sky (dir. Joe Johnston) is a wonderful example.
John Hickam plays the role of the type of father often seen in movies that plays favorites with his children and often neglects the other, but will undergo change to reflect a love of both children.