Possible subspaces

Algebra Level 3

Let VV be the vector space C2\mathbb{C}^2, or the set of vectors with two complex number components. Which of the following, if any, are subspaces of VV?

  1. The set of vectors (xy)\begin{pmatrix}x\\y\end{pmatrix} for which xy=0xy = 0.
  2. The set of vectors (xy)\begin{pmatrix}x\\y\end{pmatrix} for which xx and yy are both integers.
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