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 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?

Prove that none of the roots of the equation z^(n) = 2(1+ z+z^2 + …...+ z^(n-1)), n gt 1 , lies outside the circle |z|=3 .

If the system of equations (.^(n)C_(3))x+(.^(n)C_(4))y+35z=0, (.^(n)C_(4))x+35y+(.^(n)C_(3))z=0 and 35x+(.^(n)C_(3))y+(.^(n)C_(4))z=0 has a non - trivial solution, then the value of n is equal to (AA n in N, n ge 4)

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

if (2z-n)/(2z+n)=2i-1,n in N in N and IM(z)=10, then

Given f(1)=2 and f(n+1)=(f(n)-1)/(f(n)+1)AA n in N then

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) .

Show that the roots of equation (1+z)^n=(1-z)^n are i tan (rpi)/n, r=0,1,2,,…………,(n-1) excluding the vlaue when n is even and r=n/2

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