If `n >1` , show that the roots of the equation `z^n=(z+1)^n` are collinear.

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

If nin Ngt1, find the sum of real parts of the roots of the equation z^(n)=(z+1)^(n).

If nin Ngt1, find the sum of real parts of the roots of the equation z^(n)=(z+1)^(n).

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

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

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) .

zo is one of the roots of the equation z^n cos theta0+ z^(n-1) cos theta2 +. . . . . . + z cos theta(n-1) + cos theta(n) = 2, where theta in R , then (A) |z0| 1/2 (C) |z0| = 1/2

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