Our eyes have remained the same size.
In this sentence, I can't think what is
the role of 'the same size' ?
is it object of remained or
is it a complement ?
Please explain this to me briefly.
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I think considering it an intransitive verb is not technically wrong, but it would be more accurate to consider the verb (have) remain(ed) a linking verb.
And that would make the same size a complement.
A simple test I usually use is to replace the verb with be, if the sentence still has a similar meaning, it's quite likely that the verb is a linking verb. (But don't forget to check your dictionary, just to be sure!)