[theta in[0,2 pi]" 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)=],[" complex numbers "z_(1),z_(2),z_(3)" is non-zero then number of possible values of "theta" 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

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

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 |2z-1|=|z-2| and z_(1),z_(2),z_(3) are complex numbers such that |z_(1)-alpha| |z|d.>2|z|

If z_(1),z_(2),z_(3) are three complex numbers such that there exists a complex number z with |(:z_(1)-z|=||z_(2)-z|=|backslash z_(3)-z| show that z_(1),z_(2),z_(3) lie on a circle in the Argand diagram.

If Z_(1),Z_(2) are two complex numbers such that Z_(1)+Z_(2) is a complex no and Z_(1)Z_(2) is real number

Let z_(1), z_(2), z_(3) be three non-zero complex numbers such that z_(1) bar(z)_(2) = z_(2) bar(z)_(3) = z_(3) bar(z)_(1) , then z_(1), z_(2), z_(3)

Let z_(1)z_(2),z_(3), be three complex number such that z_(1)+z_(2)+z_(3)=0 and |z_(1)|=|z_(2)|=|z_(3)|=1 then Let |z_(1)^(2)+2z_(2)^(2)+z_(3)^(2)| equals

If az_(1)+bz_(2)+cz_(3)=0 for complex numbers z_(1),z_(2),z_(3) and real numbers a,b,c then z_(1),z_(2),z_(3) lie on a

If az_(1)+bz_(2)+cz_(3)=0 for complex numbers z_(1),z_(2),z_(3) and real numbers a,b,c then z_(1),z_(2),z_(3) lie on a