Which of the following is a complex sentence? a. eileen bought pants but not a new jacket. b. sue gave jim a new racket, and he left for the tennis courts. c. mark wanted blueberry pie and vanilla ice cream. d. as i expected, she showed up late.

For this I would choose the first choice, A. "Eileen bought pants but not a new jacket."

A complex sentence is formed by an independent and a dependent clause. An independent clause is a part of a sentence that can still be a sentence on it's own. For example, "Eileen bought pants." could be a valid sentence. 

A dependent clause is the opposite, and is a part of a sentence that can not still be a sentence on it's own. "But not a new jacket." is not a valid sentence.

I hope this was helpful.