For irrationality of root 2, I typed.

    \sqrt{2}\not\in\mathbb{Q}

It refused to accept this answer, even though it looked pixel-for-pixel identical with the intended output.

On further play...perhaps there's some small difference between \not\in and \notin, as there is clearly between \not\exists and \nexists, but I couldn't see it..

Similarly, for the inverse of a complex number, I couldn't figure out why it didn't accept:

     z^{-1} = \frac{\overline{z}}{|z|^2},\forall z \neq 0