Let S=\ z: 3 leq 2 z-3(1+i) leq 7\ be a set of complex numbers. Then Min z in S (z+1/2(5+3 i) ) is equal to :

Mathematics · Complex Numbers

JEE Main 2026 — 23 January, Morning Shift — Question 17

Let $S=\{z: 3 \leq|2 z-3(1+i)| \leq 7\}$ be a set of complex numbers. Then $\operatorname{Min}_{z \in S}\left|\left(z+\frac{1}{2}(5+3 i)\right)\right|$ is equal to :

Option A:
$\frac{1}{2}$
Option B:
$\frac{3}{2}$
Correct
Option C:
$2$
Option D:
$\frac{5}{2}$

Answer: B

Step-by-step solution

$\frac{3}{2} \leq\left|z-\frac{3}{2}(1+i)\right| \leq \frac{7}{2}$

$\operatorname{Min}_{z \in \mathrm{~s}}\left|z-\left(\frac{-5}{2}-\frac{3}{2} \mathrm{i}\right)\right|=P B$

$\mathrm{PB}=\mathrm{PC}-\frac{7}{2}$

$\Rightarrow 5-\frac{7}{2} \Rightarrow \frac{3}{2}$ Option (2)

Answer key and solution verified before publishing.

Practise Complex Numbers

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2026
Paper: 23 January, Morning Shift
Subject: Mathematics
Chapter: Complex Numbers
Topic: Introduction to Complex Numbers