If z1, z2, z3 are the roots of the equation z3-z2(1+3 i) +z(3 i-2)+2=0, then Im(z1)+Im(z2)+Im(z3) is

Question

If z1, z2, z3 are the roots of the equation z3-z2(1+3 i) +z(3 i-2)+2=0, then Im(z1)+Im(z2)+Im(z3) is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

(z3-z2-2 z+2)+3 i(z-z2)=0 (z-1)(z2-2)+3 i z(1-z)=0 (z-1)(z2-2-3 i z)=0 z=1, z=2 i, z=i Im(z1)+Im(z2)+Im(z3)=3

Q. If $z_{1}, z_{2}, z_{3}$ are the roots of the equation $z^{3} - z^{2} (1 + 3 i)$ $+ z (3 i - 2) + 2 = 0$ , then $I m (z_{1}) + I m (z_{2}) + I m (z_{3})$ is