If `z^(2) + z + 1 = 0 , z in CC ` , then `| sum_(n=1)^(15) (z^(n)+(-1)^(n)1/(z^(n)))^(2)|` is equal to ______.

If n in Z , then (2^(n))/(1+i)^(2n)+(1+i)^(2n)/(2^(n)) is equal to

|z|=1&z^(2n)+1!=0 then (z^(n))/(z^(2n)+1)-(z^(n))/(z^(2n)+1) is equal to

If z + (1)/(z) = 2 cos theta, z in "C then z"^(2n) - 2z^(n) cos (n theta) is equal to

If z_(1),z_(2),……………,z_(n) lie on the circle |z|=R , then |z_(1)+z_(2)+…………….+z_(n)|-R^(2)|1/z_(1)+1/z_(2)+…….+1/z-(n)| is equal to

If n is a positive integer but not a multiple of 3 and z=-1+i sqrt(3), then (z^(2n)+2^(n)z^(n)+2^(2n)) is equal to

If z=-2 + 2 sqrt3i then z^(2n) + z^(n) + 2^(4n) may be equal to

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