'you' is not an object (nor complement) As you suggest, 'speak' is intransitive and takes no object. 'with you' is a prepositional phrase.

Thanks Peter for the answer :))))))

'you' is a direct object and not a complement in this example. A complement would tell us something about the noun phrase. Some verbs are both intransitive and transitive. In the example the verb would be transitive but you could also use 'speak' as an intransitive verb. E.g. My mother speaks and we listen. I hope that helps!