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Complex Numbers question

2024 · 1 Feb · Shift 1 · Q36
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  5. /2024 · 1 Feb · Shift 1 · Q36

Complex Numbers question

2024 · 1 Feb · Shift 1 · Q36

JEE MainMathematicsComplex NumbersMCQ+4 / −1
Let S=∣z∈C:∣z−1∣=1\mathrm{S}=|\mathrm{z} \in \mathrm{C}:| z-1 \mid=1S=∣z∈C:∣z−1∣=1 and (2−1)(z+zˉ)−i(z−zˉ)=22∣(\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2 \sqrt{2} \mid(2​−1)(z+zˉ)−i(z−zˉ)=22​∣. Let z1,z2∈Sz_1, z_2 \in \mathrm{S}z1​,z2​∈S be such that ∣z1∣=max⁡z∈s∣z∣\left|z_1\right|=\max\limits_{z \in s}|z|∣z1​∣=z∈smax​∣z∣ and ∣z2∣=min⁡z∈S∣z∣\left|z_2\right|=\min\limits _{z \in S}|z|∣z2​∣=z∈Smin​∣z∣. Then ∣2z1−z2∣2\left|\sqrt{2} z_1-z_2\right|^2​2​z1​−z2​​2 equals :
  1. A
    1
  2. B
    4
  3. C
    3
  4. D
    2
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