Number of complex numbers satisfying `z^3 = barz` is

Let omega be the complex number cos (2 pi)/(3)+i sin (2 pi)/(3) . Then the number of distinct complex number z satisfying [[z+1,omega,omega^(2)],[omega,z+omega^2,1],[omega^(2),1,z+omega]] = 0 is equal to

Let p and q be real numbers such that p ne 0 , p^(3) ne q and p^(3) ne - q. if alpha and beta are non-zero complex numbers satisfying alpha + beta = -p and alpha^(3) + beta^(3) = q, then a quadratic equation having (alpha)/(beta ) and (beta)/(alpha) as its roots is :

If z is a complex number then

In the Argand diagram all the complex numbers z satisfying |z-4 i|+|z+4 i|=10 lie on a

If z_(1),z_(2) are two complex numbers satisfying the equation : |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then (z_(1))/(z_(2)) is a number which is

If z is a complex number satisfying z^(4)+z^(3)+2 z^(2)+z+1=0 then |z|=

Among the complex numbers, z satisfying |z+1-i| le 1 , the number having the least positive argument is :

If z is any complex number satisfying |z-1|=1 , then which of the following correct?

Let z be a complex number satisfying the equation z^(2)-(3+i)z+lambda+2i=0, whre lambdain R and suppose the equation has a real root , then find the non -real root.

The number of complex numbers z such that |z-1|=|z+1|=|z-i| equals