No believing is not a work. It is accepting and responding to the truth because I can do no other. Faith comes by hearing and hearing by the word of God.
If I walk up to you and give you $10, that is a gift which requires no belief or work on your part to receive..
However, if I walk up to you and promise to give you $10 if in return for you doing something then you only obtain the $10 by your doing something in return, which let say that something is your saying "you believe" So your faith is in receiving the $10 thus saying I believe is the works that obtains the promise.