Let zn=1 zn−1=(z−1)(z−α1)(z−α2)(z−α3)...(z−αn−1) Sum of nth roots of unity =0 ‌‌‌1+α1+α2+α3+...+αn−1=0 ‌⇒‌‌α1+α2+α3+...+αn−1=−1 Also, the coefficient of zn−1 is zero, so sum of product of zeroes taken two at a time =0 ‌⇒‌‌α1+α2+...+αn−1+