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MCQMediumJEE Main 2023 · 10 April, Shift 2Complex Numbers Basics

Mathematics Question from JEE Main 2023 · 10 April, Shift 2

Let S={ z=x+iy:2z−3i4z+2iS = \{\, z = x + iy : \frac{2z - 3i}{4z + 2i} is a real number }\} Then which of the following is NOT correct?

  • A

    y∈(−∞,−12)∪(−12,∞)y \in \left( -\infty, -\frac{1}{2} \right) \cup \left( -\frac{1}{2}, \infty \right)

  • B

    (x,y)=(0,−12)(x, y) = \left(0, -\frac{1}{2}\right)

  • C

    x=0x = 0

  • D

    y+x2+y2≠−14y + x^2 + y^2 \neq -\frac{1}{4}

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