The least value of \( |z| \) where \( z \) is complex number which ...

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The least value of \( |z| \) where \( z \) is complex number which satisfies the inequality
\( \mathrm{P} \) \( \exp \left(\frac{(|z|+3)(|z|-1)}{|| z|+1|} \log _{e} 2\right) \geq \log _{\sqrt{2}}|5 \sqrt{7}+9 i|, i=\sqrt{-1} \), is equal to:
[JEE Main-2021 (March)]
(a) 8
(b) 3
(c) 2
(d) \( \sqrt{5} \)
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