If `,Z_1,Z_2,Z_3,........Z_(n-1)` are `n^(th)` roots of unity then the value of `1/(3-Z_1)+1/(3-Z_2)+..........+1/(3-Z_(n-1))` is equal to

1,z_(1),z_(2),z_(3),......,z_(n-1), are the nth roots of unity, then (1-z_(1))(1-z_(2))...(1-z_(n-1)) is

If z_(0), z_(1),z_(2),...,z_(5) be 6^(th) roots of unity where z_(0)=1 then the value of (1)/(3)(2+z_(1))(2+z_(2))...(2+z_(5)) is...

If z_(1),z_(2),z_(3),…………..,z_(n) are n nth roots of unity, then for k=1,2,,………,n

Let 1, z_(1),z_(2),z_(3),…., z_(n-1) be the nth roots of unity. Then prove that (1-z_(1))(1 - z_(2)) …. (1-z_(n-1))= n . Also,deduce that sin .(pi)/(n) sin.(2pi)/(pi)sin.(3pi)/(n)...sin.((n-1)pi)/(n) = (pi)/(2^(n-1))

If z_(1) and z_(2) are two n^(th) roots of unity, then arg (z_(1)/z_(2)) is a multiple of

If z_1,z_2,z_3,z_4 are imaginary 5th roots of unity, then the value of sum_(r=1)^(16)(z1r+z2r+z3r+z4r),i s 0 (b) -1 (c) 20 (d) 19

If 1,z_(1),z_(2),z_(3).....z_(n-1) be n^(th) roots if unity and w be a non real complex cube root of unity, then prod_(r=1)^(n-1)(w-z_(r)) can be equal to

let z_1,z_2,z_3 and z_4 be the roots of the equation z^4 + z^3 +2=0 , then the value of prod_(r=1)^(4) (2z_r+1) is equal to :

If 1,z_(1),z_(2),z_(3),......,z_(n-1) be the n, nth roots of unity and omega be a non-real complex cube root of unity,then prod_(r=1)^(n-1)(omega-z_(r)) can be equal to

If the fourth roots of unity are z_(1),z_(2),z_(3),z_(4) and z_(1)^(2)+z_(2)^(2)+z_(3)^(2)+z_(4)^(2) is equal to :