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