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+3 votes
21.3k views
in Mathematics by (60.8k points)

For a non-zero complex number z, let arg(z) denote the principal argument with - π < arg(z) π. Then, which of the following statement(s) is (are) FALSE? 

(A) arg(-1 - i) = π/4, where i = -1 

(B) The function f : R → (-π, π ], defined by f(t) = arg(-1 + it) for all t ∈R, is continuous at all points of R, where i = -1

(C) For any two non-zero complex numbers z1 and z2,arg(z1/z2) - arg(z1) + arg(z2) is an integer multiple of 2π 

(D) For any three given distinct complex numbers z1, z2 and z3, the locus of the point z satisfying the condition arg((z -z1)(z2 - z3)/(z - z3)(z2 - z1)) = π, lies on a straight line

1 Answer

+2 votes
by (150k points)
selected by
 
Best answer

Answer (A,B,D)

solution

Discontinuous at t = 0.

=> z, z1, z2, z3 are concyclic.

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