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

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

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

zo is one of the roots of the equation z^n cos theta_0+ z^(n-1) cos theta_2 +. . . . . . + z cos theta_(n-1) + cos theta_(n) = 2 , where theta in R , then (A) |z_0| lt 1/2 (B) |z_0| gt 1/2 (C) |z_0| = 1/2 (D)None of these

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 n is a positive integer greater than unity z is a complex number satisfying the equation z^n=(z+1)^n, then

If z_1,z_2,z_3,………..z_(n-1) are the roots of the equation 1+z+z^2+…….+z^(n-1)=0, where n epsilon N, ngt2 then (A) z_1,z_2, …z_(n-1) are terms of a G.P. (B) z_1,z_2,……,z_(n-1) are terms of an A.P. (C) |z_1|=|z_2|=|z_3|=.|z_(n-1)|!=1 (D) none of these

If n in N >1 , then the sum of real part of roots of z^n=(z+1)^n is equal to

If z_1 is a root of the equation a_0z^n+a_1z^(n-1)++a_(n-1)z+a_n=3,w h e r e|a_i| 1/4 d. |z|<1/3

If z_1a n dz_2 are the complex roots of the equation (x-3)^3+1=0,t h e nz_1+z_2 equal to 1 b. 3 c. 5 d. 7

If f(x)=(x^(4)+x^(2)+1)/(x^(2)-x+1) , the value of f(omega^(n)) (where 'omega' is the non-real root of the equation z^(3)=1 and 'n' is a multiple of 3), is ……….. .