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

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

Let w(Im w!=0) be a complex number.Then the set of all complex numbers z satisfying the equal w-bar(w)z=k(1-z), for some real number k,is :

If complex number omega=(5+3z)/(5(1-z))|z|<1 then

Let Z and w be two complex number such that |zw|=1 and arg(z)-arg(w)=pi/2 then

Suppose two complex numbers z=a+ib , w=c+id satisfy the equation (z+w)/(z)=(w)/(z+w) . Then

Let z be a complex number satisfying z^(117)=1 then minimum value of |z-omega| (where omega is cube root of unity) is