`arg(z_1/z_2)=arg(z_1)-arg(z_2)`

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 for complex numbers z_(1) and z_(2),arg(z_(1))-arg(z_(2))=0 then |z_(1)-z_(2)| is equal to

If for complex numbers z_(1) and z_(2)arg(z_(1))-arg(z_(2))=0, then show that |z_(1)-z_(2)|=|z_(1)|-|z_(2)||

Let z_(1),z_(2) be two distinct complex numbers with non-zero real and imaginary parts such that "arg"(z_(1)+z_(2))=pi//2 , then "arg"(z_(1)+bar(z)_(1))-"arg"(z_(2)+bar(z)_(2)) is equal to

arg(bar(z))=-arg(z)

If z_(1) and z_(2), are two non-zero complex numbers such tha |z_(1)+z_(2)|=|z_(1)|+|z_(2)| then arg(z_(1))-arg(z_(2)) is equal to

If z_(1) and z_(2) are two non-zero complex number such that |z_(1)z_(2)|=2 and arg(z_(1))-arg(z_(2))=(pi)/(2) ,then the value of 3iz_(1)z_(2)

If |z|=1 and z ne +-1 , then one of the possible value of arg(z)-arg(z+1)-arg(z-1) , is

If z_(1),z_(2) and z_(3) are three distinct complex numbers such that |z_(1)| = 1, |z_(2)| = 2, |z_(3)| = 4, arg(z_(2)) = arg(z_(1)) - pi, arg(z_(3)) = arg(z_(1)) + pi//2 , then z_(2)z_(3) is equal to