If `arg (z_2 - z_1) + arg (z_3 - z_1) = 2 arg (z - z_1)` where `z,z_1,z_2 and z_3`, are complex numbers, then the locus of z is

If arg (z-z_1)/(z_2-z_1) = 0 for three distinct complex numbers z,z_1,z_2 then the three points are

If |z_1| = |z_2| and "arg" (z_1) + "arg" (z_2) = pi//2, , then

If arg((z-1)/(z+1))=(pi)/(2) then the locus of z is

If | z_ (1) + z_ (2) | = | z_ (1) -z_ (2) |, then arg z_ (1) -arg z_ (2) =

If arg[z_(3)-z_(2))]=arg[z_(3)(z_(2)-z_(1))], then find prove that O,z_(1),z_(2),z_(3) are concyclic, where O is the origin.

If |z_(1)+ z_(2)|=|z_(1)|+|z_(2)| , then arg z_(1) - arg z_(2) is

If z_(1),z_(2) and z_(3), z_(4) are two pairs of conjugate complex numbers, the find the value of arg(z_(1)/z_(4)) + arg(z_(2)//z_(3)) .