JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let \( S=\{z:3\le|2z-3(1+i)|\le7\} \) be a set of complex numbers. Then \( \min_{z\ \in\ S} |z+\frac{1}{2}(5+3i)| \) is equal to :
- A \( \frac{1}{2} \)
- B \( \frac{3}{2} \)
- C 2
- D \( \frac{5}{2} \)
Answer & Solution
Correct Answer
(B) \( \frac{3}{2} \)
Step-by-step Solution
Detailed explanation
\(\frac{3}{2} \leq\left|z-\frac{3}{2}(1+i)\right| \leq \frac{7}{2}\) \(\operatorname{Min}_{z\ \in\ S}\left|z-\left(\frac{-5}{2}-\frac{3}{2} i\right)\right|=P B\) \(PB = PC -\frac{7}{2} \Rightarrow 5-\frac{7}{2} \Rightarrow \frac{3}{2}\)
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