Let S=z=x+iy:2z-3i4z+2i is a real number }. Then which of the following is NOT correct?

Question

Let $S = \{z = x + i y : \frac{2 z - 3 i}{4 z + 2 i}$ is a real number $}$ . Then which of the following is NOT correct?

y + x^{2} + y^{2} \neq - \frac{1}{4}

(x, y) = (0, - \frac{1}{2})

x = 0

y \in (- \infty, - \frac{1}{2}) \cup (- \frac{1}{2}, \infty)

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