Can I just point out that it's the first question that should be closed, not the second?
Note that the assumption is that someone made a second account because they couldn't access the first. If you close the question from the second account, they still won't have access to the first account. If you close the question from the first account, they may have access to the second.
Closing the second makes it more likely that we have an orphan question that will never have an answer accepted and which doesn't respond to feedback.
Sometimes the correct thing is to close both questions, because they suck. I'm not talking about that situation but one in which the question is valid but duplicated. I'm also not talking about the situation where two different people asked the question. Just ones where it seems that some one person posted the same question twice. In that case, closing the second question as a duplicate leaves more problems than closing the first one.