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_1,z_2,z_3 are any three roots of the equation z^6=(z+1)^6, then arg((z_1-z_3)/(z_2-z_3)) can be equal to

If alpha,beta are roots of the equation x^2+3x+7=0,t h e n1//alpha+1beta is equal to 7//3 (b) -7//3 (c) 3//7 (d) -3//7

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 :

If z_1a n dz_2 are two nonzero complex numbers such that = |z_1+z_2|=|z_1|+|z_2|, then a rgz_1-a r g z_2 is equal to -pi b. pi/2 c. 0 d. pi/2 e. pi

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 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

Find the complex number satisfying the system of equations z^3+ omega^7=0a n dz^5omega^(11)=1.

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=-( z )_2dot