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

Options

A. `arg (-1-i) =pi/4 , " where " o = sqrt(-1)`
B. The function f : `Rrarr(-pi,pi)` defined by f(t) = arg (–1 + it) for all t  R, is continuous at all points of R, where `i=sqrt(-1)`
C. For any two non-zero complex numbers `z_1andz_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

Answer

A, B, D