The product of norms-norm of product
\prod_{k=1}^{n-1}||e^\frac}2\piik}{n}-1||=||\prod_{k=1}^{n-1}(e^\frac{2\piik}{n}-1)||
Let w_k=e^\frac{2\piik}{n} for roots of unity other than 1, these are the roots of the equation z^{n-1}+z^{n-2}+...+z+1=0
so,(w_k-1) is a root of
(z+1)^{n-1}+(z+1)^{n-2}+...+(z+1)+1=0 for all k.
The product of the roots of the polynomial are by Vieta's formula equal to (-1)^{n-1}\frac{a_0}{a_n} where a_0 is the coefficient on the constant term a_n is the coefficient on the leading term
leading term's coefficient is 1, the constant term is the sum of n 1's.
product is (-1)^{n-1}n and its norm is n.
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