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 z_(1) and z_(2) are the complex roots of the equation (x-3)^(3) + 1=0 , then z_(1) +z_(2) equal to

If z is complex root of the equation x^3+1=0 and (1+z)^7 = P+Qz then P + Q is

let z_1,z_2,z_3 and z_4 be the roots of the equation z^4 + z^3 +2=0 , then the value of prod_(r=1)^(4) (2z_r+1) is equal to :

The common roots of the equations z^(3)+2x^(2)+2z+1=0 and z^(2017)+z^(2018)+1=0 are

If alpha,beta are roots of the equation x^(2)+3x+7=0, then 1/ alpha+1 beta is equal to 7/3(b)-7/3(c)3/7(d)-3/7

Let z_1a n dz_2 b be toots of the equation z^2+p z+q=0, where he coefficients pa n dq may be complex numbers. Let Aa n dB represent z_1a n dz_2 in the complex plane, respectively. If /_A O B=theta!=0a n dO A=O B ,w h e r eO is the origin, prove that p^2=4q"cos"^2(theta//2)dot

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 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_(4) are the roots of the equation z^(4)+z^(3)+z^(2)+z+1=0, then the least value of [|z_(1)+z_(2)|]+1 is (where [.] is GIF.)

Let z_1 and z_2 be the roots of the equation 3z^2 + 3z + b=0 . If the origin, together with the points represented by z_1 and z_2 form an equilateral triangle then find the value of b.