If the equation `z^3 + (3 + i)(z^2) - 3z - (m + i)= 0,` `m in R` , has at least one real root, then sum of possible values of m, is

Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0\ ,where m in Rdot . Suppose the equation has a real root. Then find the value of m

Let A={a in R} the equation (1+2i)x^3-2(3+i)x^2+(5-4i)x+a^2=0 has at least one real root. Then the value of (suma^2)/2 is_______.

If z is a complex number satisfying z^4+z^3+2z^2+z+1=0 then the set of possible values of z is

If Z=(sqrt3+i)/2 ,then the value of z^69 is

theta in [0,2pi] and z_(1) , z_(2) , z_(3) are three complex numbers such that they are collinear and (1+|sin theta|)z_(1)+(|cos theta|-1)z_(2)-sqrt(2)z_(3)=0 . If at least one of the complex numbers z_(1) , z_(2) , z_(3) is nonzero, then number of possible values of theta is

If z is a complex number satisfying the equation z^6 +z^3 + 1 = 0 . If this equation has a root re^(itheta) with 90^@<0<180^@ then the value of theta is

If (1+i)^2 /(3 - i) =Z , then Re(z) =

If one root of the equation z^2-a z+a-1= 0 is (1+i), where a is a complex number then find the root.

If z =(-2)/(1+sqrt3i), then the value of arg(z) is-

If z=3i then the value of zbarz is