Let $S = \left\{ {z = x + iy:{{2z - 3i} \over {4z + 2i}}\,\mathrm{is\,a\,real\,number}} \right\}$. Then which of the following is NOT correct?

Question

$y + {x^2} + {y^2} \ne - {1 \over 4}$

$(x,y) = \left( {0, - {1 \over 2}} \right)$

$x = 0$

$y \in \left( { - \infty , - {1 \over 2}} \right) \cup \left( { - {1 \over 2},\infty } \right)$

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