1.If ω0,ω1,…,ωn−1\omega_0, \omega_1, \ldots, \omega_{n-1}ω0,ω1,…,ωn−1 are the nthn^{th}nth roots of unity, then (1+2ω0)(1+2ω1)(1+2ω2)…(1+2ωn−1)=(1 + 2\omega_0)(1 + 2\omega_1)(1 + 2\omega_2)\ldots(1 + 2\omega_{n-1}) =(1+2ω0)(1+2ω1)(1+2ω2)…(1+2ωn−1)=a.1+(−1)n2n1 + (-1)^n 2^n1+(−1)n2nb.1+2n1 + 2^n1+2nc.(−1)n+2n(-1)^n + 2^n(−1)n+2nd.1+(−1)n−12n1 + (-1)^{n-1} 2^n1+(−1)n−12nLogin to continueOnly logged in users canattempt or see the solution.
