For every positive integer $n \geq 2$, Prove that there is no $n-$tuple of distinct complex numbers $(x_1,x_2,\dots,x_n)$ such that for each $1 \leq k \leq n$ following equality holds. $\prod_{\underset{i \neq k}{1 \leq i \leq n}}^{ } (x_k - x_i) = \prod_{\underset{i \neq k}{1 \leq i \leq n}}^{ } (x_k + x_i) $ (20 points)