Is f(z)+i arg(z) an analytic function?

AI Thread Summary
The function f(z) + i arg(z) is discussed in terms of its analyticity, with references made to the definition of log(z). It is noted that log(z) is analytic in simply connected domains excluding zero. The conversation emphasizes the need to separate ln(z) and arg(z) to assess the function's analyticity. Additionally, ln|z| is identified as the real logarithm. The conclusion is that understanding these components is crucial for determining the function's analytic nature.
Huns
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Is this function analytic or not? Please explain
 
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Well, it's the definition of log(z).
 
Svein said:
Well, it's the definition of log(z).
so how to split ln (z) and arg (z) for determining analyticity?
 
Huns said:
so how to split ln (z) and arg (z) for determining analyticity?
log(z) is analytic in any simply connected domain that does not include 0.

By the way, the expression ln|z| is the real logarithm.
 

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