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Complex Numbers question

2023 · 10 Apr · Shift 2 · Q21

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PYQ Library
JEE Main
Mathematics
Complex Numbers
2023 · 10 Apr · Shift 2 · Q21

Complex Numbers question

2023 · 10 Apr · Shift 2 · Q21

JEE MainMathematicsComplex NumbersMCQ+4 / −1

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?

A
$y + {x^2} + {y^2} e - {1 \over 4}$
B
$(x,y) = \left( {0, - {1 \over 2}} \right)$
C
$x = 0$
D
$y \in \left( { - \infty , - {1 \over 2}} \right) \cup \left( { - {1 \over 2},\infty } \right)$

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