If equation `(z- 1)^n =Z^n= 1 (n in N)` has solutions, then n can be

In equation (Z - 1)^(n) = Z^(n) = 1 (AA n in N) has solution, then n can be

If z_(1),z_(2),z_(3),…,z_(n-1) are the roots of the equation z^(n-1)+z^(n-2)+z^(n-3)+…+z+1=0 , where n in N, n gt 2 and omega is the cube root of unity, then

If z_(1),z_(2),z_(3),…,z_(n-1) are the roots of the equation z^(n-1)+z^(n-2)+z^(n-3)+…+z+1=0 , where n in N, n gt 2 and omega is the cube root of unity, then

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

{ n (n+1) (2n+1) : n in Z} sub

Let n be a positive integer and a complex number with unit modulus is a solution of the equation Z^n+Z+1=0 , then the value of n can be

Let n be a positive integer and a complex number with unit modulus is a solution of the equation Z^n+Z+1=0 , then the value of n can be

Prove that, for integral value of n ge1 , all the roots of the equation nz^(n) =1 + z+ z^2 +….+z^(n) lie within the circle |z|=(n)/(n-1) .

The roots of the equation z^(n)=(z+3)^(n)

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?