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MathsJEE Main 23 Jan 2026, Shift 1·Q17·MCQ·Moderate

Complex Numbers · Locus and minimum modulus

Let S={z:3≤∣2z−3(1+i)∣≤7}S = \{z : 3 \le \lvert 2z - 3(1 + i)\rvert \le 7\} be a set of complex numbers. Then min⁡z∈S∣(z+12(5+3i))∣\displaystyle\min_{z\in S}\left\lvert\left(z + \frac12(5 + 3i)\right)\right\rvert is equal to:
  1. (1)12\dfrac12
  2. (2)32\dfrac32
  3. (3)2
  4. (4)52\dfrac52

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See the full 23 Jan 2026, Shift 1 paper