(a) Prove that the function f(z) = Arg(z) is discontinuous at every point on the negative...

(a) Prove that the function f(z) = Arg(z) is discontinuous at every point on the negative real axis.

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(b) Prove that the function f1 defined by

is a branch of the multiple-valued function F(z) = arg(z). [Hint: See Example.]

EXAMPLE A Branch of F (z)=z1/2

FIGURE 3.1.6 The domain D of the branch f1