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_(1),z_(2),z_(3) andz_(4) are the roots of the equation z^(4)=1, the value of sum_(i=1)^(4)zi^(3) is

If z_(1),z_(2),z_(3),z_(4) are the roots of equation z^(4)+z^(3)+z^(2)+z+1=0, then prod_(i=1)^(4)(z_(i)+2)

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.

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 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 z_1,z_2,z_3,z_4 are imaginary 5th roots of unity, then the value of sum_(r=1)^(16)(z1r+z2r+z3r+z4r),i s 0 (b) -1 (c) 20 (d) 19

If z_1,z_2,z_3,z_4 are imaginary 5th roots of unity, then the value of sum_(r=1)^(16)(z1r+z2r+z3r+z4r),i s 0 (b) -1 (c) 20 (d) 19

If z_(1),z_(2),z_(3),z_(4) are roots of the equation a_(0)z^(4)+a_(1)z^(3)+a_(2)z^(2)+a_(3)z+a_(4)=0, where a_(0),a_(1),a_(2),a_(3) and a_(4) are real,then