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Why does Arg'[1. + I] return -0.5?

From the document we know that

Arg[z] gives the gives the argument of the complex number z.

Then how about Arg'[z]? This seems to be meaningless, but Mathematica returns something if z is a non-exact number, for example

Arg'[1. + I]
(* -0.5 *)

So my question is:

  1. How is the numeric value of Arg'[z] defined?

  2. Why does Arg' behave like this? What's the potential usage of this behavior?