`|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=costheta+isintheta , then (z^(2n)-1)/(z^(2n)+1)

Let z_1, z_2, …...z_n be a sequence of complex numbers defined by z_1=-1-i and z_(n+1) = z_(n)^(2) -i for all n ge 1 , then |z_(2013)| is equal to

If z_(1), z_(2),……..,z_(n) are complex numbers such that |z_(1)| = |z_(2)| = …….. = |z_(n)| = 1 , then |z_(1) + z_(2) +……..+ z_(n)| is equal to a) |z_(1)z_(2)z_(3)…..z_(n)| b) |z_(1)|+|z_(2)|+…….+|z_(n)| c) |(1)/(z_(1)) + (1)/(z_(2)) + ……….+ (1)/(z_(n))| d)n

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 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 z+1/z=2cos theta, prove that |(z^(2n)-1)/(z^(2n)+1)|=|tan n theta|