The way this is put gives rise to confusion because imagining and conceiving are not really the same thing. (It is true that, sometimes “imagine” is used to mean pretty much the same thing as “conceive,” but, more typically, it has rather richer connotations.) It seems fairly clear to me that we can conceive of nothing in the sense that we can form a concept of it - people are discussing it in this thread, after all, and as begbert2 has pointed out, we can formalize it with notions such as the empty set (or, come to that, zero), and it even turns out to be of practical use in endeavors such as mathematics and computer programming. (Sometimes it is possible to talk about things, such as circular squares, that we cannot really conceive, because the concept is self-contradictory. However, the successful formalization shows that this is not the case with nothing.)
It is much less clear, however, whether we can imagine nothing, in the sense of having some sort of quasi-sensual, vicarious experience of it, as for instance, I can imagine a unicorn, or what it would feel like to win the lottery. I very much doubt whether it is possible to imagine nothing in this sense. The imagination, it seems to me, needs some at least potentially experiencable qualities to latch on to, and nothing, by definition, does not have any (not even spatial extension).
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Infinity* is another example of something of which we can conceive (and find it useful to conceive) but cannot truly imagine. No doubt there are other examples, but my brain is too tired to think of them at the moment.
In any case, some of the people in this thread seem to be talking past one another because some are talking primarily about conceiving and some are talking about imagining in its richer (and more usual) sense.