The problem involves determining the natural domain for the function f(z) = log(log(z)), where log(z) is defined using the principal branch of the logarithm function with the argument constrained to -π < arg(z) < π.
The discussion is ongoing, with participants raising questions about the conditions under which log(z) is a negative real number and the implications for defining the function f(z). Some guidance has been offered regarding the need to avoid certain values of z, but no consensus has been reached.
There is a mention of potential terminology issues regarding the characterization of log(z) being zero and its relevance to the domain of f(z).
justin_huang said:I already know how to represent the arg z by arctanb/a+2pi*k
how can I get arctan [Re (log z)/Im (log z)]+2pi*k
or any other method?
micromass said:The "[itex]+2\pi k[/itex] shouldn't be here right?
So basically, you want to know when
[tex]-\pi<arg(log(z))<\pi[/tex]
surely this correspond to log(z) being a negative real number.
So, you must calculate log(z) in some way (do you have a formula for it) and see when it is a negative real number. These are the z we don't want.