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Complex Numbers question

2022 · 29 Jul · Shift 2 · Q34

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PYQ Library
JEE Main
Mathematics
Complex Numbers
2022 · 29 Jul · Shift 2 · Q34

Complex Numbers question

2022 · 29 Jul · Shift 2 · Q34

JEE MainMathematicsComplex NumbersMCQ+4 / −1

Let

\mathrm{S}=\{z=x+i y:|z-1+i| \geq|z|,|z|\lt 2,|z+i|=|z-1|\}

. Then the set of all values of

x

, for which

w=2 x+i y \in \mathrm{S}

for some

y \in \mathbb{R}

, is :

A
$\left(-\sqrt{2}, \frac{1}{2 \sqrt{2}}\right]$
B
$\left(-\frac{1}{\sqrt{2}}, \frac{1}{4}\right]$
C
$\left(-\sqrt{2}, \frac{1}{2}\right]$
D
$\left(-\frac{1}{\sqrt{2}}, \frac{1}{2 \sqrt{2}}\right]$

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