If the equation `|z(z+1)^8 =z^8 |z+1|` where `z in C and z(z+1) != 0` has distinct roots `z_1,z_2,z_3,...,z_n`.(where `n in N`) then which of the following is/are true?

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

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

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

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

If |z_(1)| = |z_(2)| = |z_(3)| = … |z_(n)| = 1 , then |z_(1) + z_(2) + z_(3) + ….. + z_(n) | =

If z is a complex number satisfying z + z^-1 = 1 then z^n + z^-n , n in N , has the value

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

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

If |z|=2a n d(z_1-z_3)/(z_2-z_3)=(z-2)/(z+2) , then prove that z_1, z_2, z_3 are vertices of a right angled triangle.