Verified Solution • 2025–26 Session
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QJEEM22Ma5e2c: JEE Main 2022 Mathematics - Class 11 JEEM22Ma5e2c Solution: Let S = { z = x + i y :
Let
Multiple Choice Options
- A (−2,122]
- B (−12,14]
- C (−2,12]
- D (−12,122]
Step-by-Step Verified Solution
S:\{z=x+i y:|z-1+i| \geq|z|,|z|<2,|z-i|=|z-1|\}
|z|<2
and
2 x<\frac{1}{2} \quad\quad \therefore x<\frac{1}{4}
(2 x)^{2}+(-2 x)^{2}<4
4 x^{2}+4 x^{2}<4
x^{2}<\frac{1}{2} \Rightarrow x \in\left(-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)
|z|<2
and
2 x<\frac{1}{2} \quad\quad \therefore x<\frac{1}{4}
(2 x)^{2}+(-2 x)^{2}<4
4 x^{2}+4 x^{2}<4
x^{2}<\frac{1}{2} \Rightarrow x \in\left(-\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)