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JEE Main 202623 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
23 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Complex Number

JEE Main 2026 · 23 January · Morning Shift · Mathematics · Complex Number

Let S=\ z: 3 ≤|2 z-3(1+i)| ≤ 7\ be a set of complex numbers. Then _...

Let S={z:3⩽∣2z−3(1+i)∣⩽7}S=\{z: 3 \leqslant|2 z-3(1+i)| \leqslant 7\} be a set of complex numbers. Then min⁡z∈S\min _{z \in S}\left|\left(z+\frac{1}{2}(5+3 i)\right)\right| is equal to :Let S=\ z: 3 ≤|2 z-3(1+i)| ≤ 7\ be a set of complex numbers. Then _ z ∈ S | (z+(1)/(2)(5+3 i))| is equal to :

Options

  1. A2
  2. B52\frac{5}{2}
  3. C32\frac{3}{2}
  4. D12\frac{1}{2}

Correct answer

C. 32\frac{3}{2}

Step-by-step solution

32≤∣z−32(1+i)∣≤72\dfrac{3}{2} \leq \left| z - \dfrac{3}{2}(1+i) \right| \leq \dfrac{7}{2}
Let S=\ z: 3 ≤|2 z-3(1+i)| ≤ 7\ be a set of complex numbers. Then _ z ∈ S | (z+(1)/(2)(5+3 i))| is equal to :
min⁡z∈S∣z−(−52−32i)∣=PB\min_{z \in S} \left| z - \left(\dfrac{-5}{2} - \dfrac{3}{2}i\right) \right| = PB
PB=PC−72⇒5−72⇒32PB = PC - \dfrac{7}{2} \Rightarrow 5 - \dfrac{7}{2} \Rightarrow \dfrac{3}{2}
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