If `z_(1)`, `z_(2)`, `z_(3)` are any three complex numbers on Argand plane, then `z_(1)(Im(barz_(2)z_(3)))+z_(2)(Imbarz_(3)z_(1)))+z_(3)(Imbarz_(1)z_(2)))` is equal to

If z_(1), z_(2), z_(3) are three complex numbers in A.P., then they lie on

If z_(1),z_(2),z_(3) are the vertices of an equilateral triangle in the Argand plane, then (z_(1)^(2)+z_(2)^(2)+z_(3)^(3))=lambda(z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)) holds true when :

For any two complex numbers z_(1) and z_(2) , prove that Re ( z_(1)z_(2)) = Re z_(1) Re z_(2)- 1mz_(1) Imz_(2)

For any two complex numbers, z_(1),z_(2) |1/2(z_(1)+z_(2))+sqrt(z_(1)z_(2))|+|1/2(z_(1)+z_(2))-sqrt(z_(1)z_(2))| is equal to

If z_(1),z_(2),z_(3) are complex numbers such that : |z_(1)|=|z_(2)|=|z_(3)|=|(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))|=1 , then |z_(1)+z_(2)+z_(3)| is equal to

If z_(1), z_(2) are two complex numbers such that Im(z_(1)+z_(2))=0 and Im(z_(1) z_(2))=0 , then

|z_(1)+z_(2)|=|z_(1)|+|z_(2)| is possible if

If z_(1),z_(2),z_(3) represent the vertices of an equilateral triangle such that |z_(1)|=|z_(2)|=|z_(3)| , then

Let z_(1)z_(2)andz_(3) be three complex numbers and a,b,cin R, such that a+b+c=0andaz_(1)+bz_(2)+cz_(3)=0 then show that z_(1)z_(2)and z_(3) are collinear.

If z_(1) and z_(2) are two non-zero complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| , then arg. z_(1)- arg. z_(2) equals :