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

[Huns]

Is this function analytic or not? Please explain

 

[Svein]

Well, it's the definition of log(z).

 

[Huns]

Well, it's the definition of log(z).

so how to split ln (z) and arg (z) for determining analyticity?

 

[Svein]

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.