If for complex numbers `z_1 and z_2, |z_1+z_2|=|z_1|=|z_2|` then `argz_1-argz_2=` (A) an even multiple of `pi` (B) an odd multiple of `pi ` (C) an odd multiple of `pi/2` (D) none of these

If z_1 and z_2 are two non zero complex number such that |z_1+z_2|=|z_1|+|z_2| then arg z_1-argz_2 is equal to (A) - pi/2 (B) 0 (C) -pi (D) pi/2

| z_ (1) + z_ (2) | = | z_ (1) | - | z_ (2) |, thenarg z_ (1) -argz_ (2) =

Complex number z_1 and z_2 satisfy z+barz=2|z-1| and arg (z_1-z_2) = pi/4 . Then the value of lm (z_1+z_2) is

For a non-zero complex number z , let arg(z) denote the principal argument with pi lt arg(z)leq pi Then, which of the following statement(s) is (are) FALSE? arg(-1,-i)=pi/4, where i=sqrt(-1) (b) The function f: R->(-pi, pi], defined by f(t)=arg(-1+it) for all t in R , is continuous at all points of RR , where i=sqrt(-1) (c) For any two non-zero complex numbers z_1 and z_2 , arg((z_1)/(z_2))-arg(z_1)+arg(z_2) is an integer multiple of 2pi (d) For any three given distinct complex numbers z_1 , z_2 and z_3 , the locus of the point z satisfying the condition arg(((z-z_1)(z_2-z_3))/((z-z_3)(z_2-z_1)))=pi , lies on a straight line

If z_1 , z_2 are nonreal complex and |(z_1+z_2)/(z_1-z_2)| =1 then (z_1)/(z_2) is

If |z_1+z_2| = |z_1-z_2| , prove that amp z_1 - amp z_2 = pi/2 .

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

if |z_1| = |z_2| ne 0 and amp (z_1)/(z_2) = pi then

The complex number z satisfying |z+1|=|z-1| and arg (z-1)/(z+1)=pi/4 , is