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

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

If 1 , z_1 , z_2 ,......., z_6 are the 7th roots of unity then the value of (2-z_1)(2-z_2)(2-z_3)(2-z_4)(2-z_5)(2-z_6)= (a) 63 b. 127 c. 32 d. 31

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))

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,ddotz_(19) are the 20th roots of unity then (1-z_1)(1-z_2)(1-z_3)...(1-z_(19))= 0 2. 19 3. 20 4. 1 5. 10

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

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 z_1,z_2,z_3,………..z_(n-1) are the roots of the equation 1+z+z^2+…….+z^(n-1)=0, where n epsilon N, ngt2 then (A) z_1,z_2, …z_(n-1) are terms of a G.P. (B) z_1,z_2,……,z_(n-1) are terms of an A.P. (C) |z_1|=|z_2|=|z_3|=.|z_(n-1)|!=1 (D) none of these