https://en.wikipedia.org/wiki/Complement_(linguistics) Construed in the broadest sense, any time a given expression is somehow necessary in order to render another expression "complete", it can be characterized as a complement of that expression:
with *the class* – The NP the class is the complement of the preposition, with. Jim will *help*. – The main verb help is the complement of the auxiliary verb, will. Chris gave *up*. – The particle up is the complement of the verb gave. as *a friend* – The NP a friend is the complement of the preposition, as. (Radford, English syntax: An introduction.)
Construed in the broad sense, many complements cannot be understood as arguments. The argument concept is tied to the predicate concept in a way that the complement concept is not.
In linguistics, an adjunct is an optional, or structurally-dispensable, part of a sentence, clause, or phrase that, when it is removed, will not affect the remainder of the sentence except to discard from it some auxiliary information.
