The least value of |z| where z is complex number which satisfies the inequality
exp \(\bigg(\frac{(|z|+3)(|z|-1)}{\big||z|+1 \big|}log_{e^2}\bigg)\) \(\geq log_\sqrt{2}\big|5\sqrt{7}+9i \big|,\)
\(i=\sqrt{-1},\) is equal to:
(1) 3
(2) \(\sqrt{5}\)
(3) 2
(4) 8
