JEE Main 202229 Jul, Evening shiftMathematicsHardComplex Numbers and Quadratic Equations264× since 2002Let S={z=x+iy:∣z−1+i∣≥∣z∣,∣z∣<2,∣z+i∣=∣z−1∣}\mathrm{S}=\{z=x+i y:|z-1+i| \geq|z|,|z|<2,|z+i|=|z-1|\}S={z=x+iy:∣z−1+i∣≥∣z∣,∣z∣<2,∣z+i∣=∣z−1∣}. Then the set of all values of xxx, for which w=2x+iy∈Sw=2 x+i y \in \mathrm{S}w=2x+iy∈S for some y∈Ry \in \mathbb{R}y∈R, is :AOption A. (−2,122]\left(-\sqrt{2}, \frac{1}{2 \sqrt{2}}\right](−2,221]BOption B. (−12,14]\left(-\frac{1}{\sqrt{2}}, \frac{1}{4}\right](−21,41]COption C. (−2,12]\left(-\sqrt{2}, \frac{1}{2}\right](−2,21]DOption D. (−12,122]\left(-\frac{1}{\sqrt{2}}, \frac{1}{2 \sqrt{2}}\right](−21,221]CheckSkip · show solution
