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

Let omega be the complex number cos((2pi)/3)+isin((2pi)/3) . Then the number of distinct complex numbers z satisfying Delta=|(z+1,omega,omega^2),(omega,z+omega^2,1),(omega^2,1,z+omega)|=0 is

Numbers of complex numbers z, such that abs(z)=1 and abs((z)/bar(z)+bar(z)/(z))=1 is

Show that the complex number z, satisfying the condition arg((z-1)/(z+1))=(pi)/(4) lie son a circle.

Consider two complex number z and omega satisfying |z|= 1 and |omega-2|+|omega-4|=2 . Then which of the following statements(s) is (are) correct?

If z is any complex number satisfying abs(z-3-2i) le 2 , where i=sqrt(-1) , then the minimum value of abs(2z-6+5i) , is

A relation R on the set of complex numbers is defined by z_1 R z_2 if and oly if (z_1-z_2)/(z_1+z_2) is real Show that R is an equivalence relation.

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

Find the all complex numbers satisying the equation 2|z|^(2)+z^(2)-5+isqrt(3)=0, wherei=sqrt(-1).

Among the complex numbers z which satisfies |z-25i|<=15 , find the complex numbers z having least positive argument.

If z is a complex number satisfying the relation ∣z+1∣=z+2(1+i) then z is