Does the statement "By God, you will not complete it" constitute an oath necessitating expiation, given that the speaker was in a state of anger and did not intend to swear an oath?

If the oath was uttered by your tongue unintentionally, it falls under the category of a 'vain oath' (laghw al-yameen), for which there is no expiation. However, if you intended the oath and your heart affirmed it, then your oath is binding, and you have broken it. Therefore, expiation (kaffarah (definition)) is required, which is: feeding ten poor persons, or clothing them, or freeing a slave. If you cannot find any of these, then you must fast for three days. Provocation does not have an effect as long as you are aware of what you are saying.