JEE Main 202310 Apr, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002Let S={z=x+iy:2z−3i4z+2i is a real number}S = \left\{ {z = x + iy:{{2z - 3i} \over {4z + 2i}}\,\mathrm{is\,a\,real\,number}} \right\}S={z=x+iy:4z+2i2z−3iisarealnumber}. Then which of the following is NOT correct?AOption A. y+x2+y2≠−14y + {x^2} + {y^2} \ne - {1 \over 4}y+x2+y2=−41BOption B. (x,y)=(0,−12)(x,y) = \left( {0, - {1 \over 2}} \right)(x,y)=(0,−21)COption C. x=0x = 0x=0DOption D. y∈(−∞,−12)∪(−12,∞)y \in \left( { - \infty , - {1 \over 2}} \right) \cup \left( { - {1 \over 2},\infty } \right)y∈(−∞,−21)∪(−21,∞)CheckSkip · show solution
