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Complex Numbers question

2022 · 28 Jul · Shift 1 · Q34
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  5. /2022 · 28 Jul · Shift 1 · Q34

Complex Numbers question

2022 · 28 Jul · Shift 1 · Q34

JEE MainMathematicsComplex NumbersMCQ+4 / −1
Let S1={z1∈C:∣z1−3∣=12}S_{1}=\left\{z_{1} \in \mathbf{C}:\left|z_{1}-3\right|=\frac{1}{2}\right\}S1​={z1​∈C:∣z1​−3∣=21​} and S2={z2∈C:∣z2−∣z2+1∣∣=∣z2+∣z2−1∣∣}S_{2}=\left\{z_{2} \in \mathbf{C}:\left|z_{2}-\right| z_{2}+1||=\left|z_{2}+\right| z_{2}-1||\right\}S2​={z2​∈C:∣z2​−∣z2​+1∣∣=∣z2​+∣z2​−1∣∣}. Then, for z1∈S1z_{1} \in S_{1}z1​∈S1​ and z2∈S2z_{2} \in S_{2}z2​∈S2​, the least value of ∣z2−z1∣\left|z_{2}-z_{1}\right|∣z2​−z1​∣ is :
  1. A
    0
  2. B
    12\frac{1}{2}21​
  3. C
    32\frac{3}{2}23​
  4. D
    52\frac{5}{2}25​
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