JEE Mains · Maths · STD 11 - 4.1 complex nubers
The least value of \(|z|\) where \(z\) is complex number which satisfies the inequality \(\exp \left(\frac{(|z|+3)(|z|-1)}{|| z|+1|} \log _{ e } 2\right) \geq \log _{\sqrt{2}}|5 \sqrt{7}+9 i |\) \(i=\sqrt{-1},\) is equal to :
- A \(3\)
- B \(\sqrt{5}\)
- C \(2\)
- D \(8\)
Answer & Solution
Correct Answer
(A) \(3\)
Step-by-step Solution
Detailed explanation
\(\exp \left(\frac{(|z|+3)(|z|-1)}{|| z|+1|} \ell\right.\) n \(\left.2\right) \geq \log _{\sqrt{2}}|5 \sqrt{7}+9 i|\) \(\Rightarrow \quad 2^{\frac{(|z|+3)(|z|-1)}{(|z|+1)} \geq \log _{\sqrt{2}}(16)}\) \(\Rightarrow \quad 2^{\frac{(|z|+3)(|z|-1)}{(|z|+1)} \geq 2^{3}}\)…
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