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 :

For any complex numbers z_1,z_2 and z_3, z_3 Im(bar(z_2)z_3) +z_2Im(bar(z_3)z_1) + z_1 Im(bar(z_1)z_2) is

If z_(1),z_(2),z_(3) are three complex numbers, such that |z_(1)|=|z_(2)|=|z_(3)|=1 & z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0 then |z_(1)^(3)+z_(2)^(3)+z_(3)^(3)| is equal to _______. (not equal to 1)

If z_(1),z_(2),z_(3),z_(4) are two pairs of conjugate complex numbers, then arg(z_(1)/z_(3)) + arg(z_(2)/z_(4)) is

If z_(1), z_(2) and z_(3) are the vertices of a triangle in the argand plane such that |z_(1)-z_(2)|=|z_(1)-z_(3)| , then |arg((2z_(1)-z_(2)-z_(3))/(z_(3)-z_(2)))| is

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) and z_(3) be unimodular complex numbers, then the maximum value of |z_(1)-z_(2)|^(2)+|z_(2)-z_(3)|^(2)+|z_(3)-z_(1)|^(2) , is

If A(z_(1)),B(z_(2)) and C(z_(3)) are three points in the Argand plane such that z_(1)+omegaz_(2)+omega^(2)z_(3)=0 , then

For any two complex numbers z_1 and z_2 , prove that Re(z_1z_2)=Re(z_1) Re(z_2)-Im(z_1) Im(z_2) .

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