Complements (that is, Subject Complements) follow linking verbs:
any form of the verb 'to be' [am, is, are, was, were, has been, are being, might have been, etc.]
and
become
seem
'has' on its own is not a linking verb and doesn't have a Subject Complement.
When books talk about objects, they usually talk about 'the thing being acted upon'. This fine for such verbs ass, "He hit me" ; but it might be better to talk about 'the person or thing toward which the action of a verb is directed '.
Hence, the action of 'having/owning/possessing' is directed at "nose".
Note: verbs do not "govern" objects. (Prepositions do govern nouns and pronouns.)
I'm a bit confused between objects and complements.
Can someone explain why in the sentence: "Jared has a big nose", 'nose' is the object?
I'm confused because nothing acts upon 'nose'. I can't see how 'nose' is governed by the verb.
To me it seems more like a complement because it links to the subject; although 'nose' doesn't equate to 'Jared'.
Thanks in advance,
First, it's important to grasp that an object is one kind of complement. Obligatory items are always complements: they are needed to complete the verb phrase. In your example "a big nose" is obligatory and thus must be a complement.
Another common kind of complement is a 'predicative complement', typically a word or phrase that is linked to the subject by the verb and which (put simply) describes the subject, e.g. "Mike is a genius". But clearly Jared is not a big nose (though he may have one!) so that rules it out as being a predicative complement.
In your example, "a big nose" is said to be an object because it is being directly acted on by virtue of being 'possessed' by Jared.