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).

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) .

A root of unity is a complex number that is a solution to the equation,z^(n)=1 for some positive integer nNumber of roots of unity that are also the roots of the equation z^(2)+az+b=0, for some integer a and b is

Find the roots of z^n = (z + 1)^n and show that the points which represent them are collinear. Hence show that these roots are also the roots of the equation, (2sin.(mpi)/(n))^2bar(z)^2+(2sin.(mpi)/n)^2bar(z)+1=0 where m = 1 , 2, 3, ..... (n-1)& |z| is finite.

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 .

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)