Donna became quickly irritated.
I'm confused about the position of "irritated". Is that considered as a direct object as it answered the verb "became"?
I read it is a complement, why? Which type?
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"become" is a linking verb, so "irritated" is indeed its subject complement. It can't be an object, as it is not a noun.
You can see more examples here: https://www.chompchomp.com/terms/subjectcomplement.htm
BTW, it should be "considered to be a direct object", not "considered as a direct object".