1.
The least value of z|z|, where zz is a complex number which satisfies the inequality e((z+3)(z1)z+1loge2)log257+9ie^{\left(\frac{(|z|+3)(|z|-1)}{|z|+1|\,\log_e 2}\right)} \geq \log_{\sqrt{2}}|5\sqrt{7} + 9i|, i=1i = \sqrt{-1}, is equal to: