JEE Main 2022 · 29 Jul · Shift 2, Mathematics question 17

Conditions. $|z-1+i|\ge|z|$ is $y\ge x-1$; $|z+i|=|z-1|$ is $y=-x$.

For w = 2x + iy: $y=-2x$, then $-2x\ge2x-1$ gives $x\le\frac14$, and $|w|^2=8x^2<4$ gives $|x|<\frac1{\sqrt2}$.

(B)