How to reply to question tags

English is not my native-tongue, so I always find it hard to grasp the concept of "question tags" and more importantly the way to answer to them. Let me explain with the help of this situation -

I am supposed to complete my homework and I haven't. My mom suspects that I haven't and asks me the below question. I want to confess that I haven't. What should I answer?

Mom : You didn't finish your homework, did you?

Me : Yes, I haven't [OR] No, I haven't?

I've always thought that it is "Yes, I haven't" because the questioner has already found out that I haven't and I should just assert it by saying 'Yes'. But a friend of mine says that it is "No, I haven't" because I am effectively answering the question "did you?".

Which of us is correct?

Answer

When someone asks a question by stating a negative fact, it would seem logical to answer affirmatively because the fact is true. However, it is more common to answer negatively to confirm the negativity.

Mom: You didn't finish your homework, did you?

You: No, I didn't

Mom: You finished your homework, didn't you?

You: No, I didn't

In both cases the Mom wants to know about the status of the homework and the questions are equivalent to

Mom: Did you finish your homework?

(The reason to use the tag form is to communicate the speaker's assumptions or surprise or expectations about the homework rather than just asking for a status update).

There is more explanation about this here.