In the sentence "complain" has no object and is therefore intransitive, as indeed it always is. The main clause is "Students complain" and the subordinate clause "the teacher does not give enough homework" in which the subject is "teacher" and the object "enough homework".
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WHIZZOIs this a case in which the verb complain is a transitive verb?It's matter of terminology and depends on what one wants to call an object. In Scandinavian grammatical terminology a clause can be the object of a verb: