Show that if `iz^3+z^2-z+i=0`, then `|z|=1`

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 8iz^(3)+12z^(2)-18z+27i=0 then 2|z|=

If 8iz^3+12z^2-18z+27i=0, then (a). |z|=3/2 (b). |z|=2/3 (c). |z|=1 (d). |z|=3/4

Show that if z_(1)z_(2)+z_(3)z_(4)=0 and z_(1)+z_(2)=0 ,then the complex numbers z_(1),z_(2),z_(3),z_(4) are concyclic.

Let A = {z : z in C, iz^(3) + z^(2) -z + i=0} and B ={z : z in C, |z|=1} , Then

If z = 3-5i then show that z^3 -10z^2+58z -136=0

If iz^(3)+z^(2)-z+i=0, where i=sqrt(-1) then |z| is equal to 1 (b) (1)/(2)(c)(1)/(4) (d) None of these