If `alpha` is a root of `z^5 +z^3 +2+3=0`, then

If alpha is a root of z^5 +z^3 +z+3=0 , then

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 :

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 :

Let z_(1), z_(2), z_(3) be the roots of iz^(3) + 5z^(2) - z + 5i = 0 , then |z_(1)| + |z_(2)| + |z_(3)| = _____________.

If alpha,beta in R are such that 1-2i (here i^(2)=-1 ) is a root of z^(2)+alpha z+beta=0 , then (alpha-beta) is equal to:

If alpha,beta are roots of z^(2)sin^(2)theta-z sin2 theta+1=0 where '0

If (1 – i) is a root of the equation , z^3 - 2 (2 - i) z^2 + (4 - 5 i) z - 1 + 3 i = 0 , then find the other two roots.