 The term complement is used to refer to an obligatory element in a construction. According to a traditional approach, complements are in a copular relationship with two other functional elements, the subject or the object. Here are two examples. In Helen is now a student of maths. A student of maths is a subject complement. Whereas in they call him a genius, a genius is the object complement. So the subject complement relates to the subject and the object complement relates to the direct object. In our examples, the complement is formally realised by a noun phrase. Other options are adjectival phrases or nominal clauses. In order to identify complements, two ways are generally suggested. Subject complements are normally in an intensive relationship with the subject and share its grammatical properties. For example, number. Object complements as noun phrases cannot become the subject of corresponding passive sentences, unlike objects themselves. Thus a genius cannot become the subject, whereas the object him can surface as the subject in a corresponding passive. By the way, if you replace a genius by a cab, it works. Because a cab is not an object complement but a second object. In X bar syntax, the phrase structure representation format in generative grammar, the term complement is used for all obligatory elements of clause structure. They are defined as sisters of the head X of a phrase and as daughters of the projection X bar of the head. So in Brutus stabbed Caesar with a knife, the noun phrase Caesar, the object of stab, is a complement. It is a sister to verb and a daughter to verb bar.