Question on what role this infinitive plays in the sentence?
In the sentence 'I am going to study", "to study" acts as the verb in fact. 'I' is the subject and as far as " To be going to" is concerned, it plays itself the role of an auxiliary verb expressing the action in a very near future. In consequence, there is no complement in this sentence, which solely composed of a subject and a verb, lacks to be meaningful.