Branch Cut for (lnz)^2: Determining Branch Points and Range

[CrimsonFlash]

Homework Statement

It is simply the same as the one for lnz i.e. does it go from 0 to ∞?
Also, is there any proper way to figure out branch points of a function?

Homework Equations

The Attempt at a Solution

 

[CrimsonFlash]

bump?

 

[Mandelbroth]

Homework Statement

It is simply the same as the one for lnz i.e. does it go from 0 to ∞?
Also, is there any proper way to figure out branch points of a function?

Do you mean, "Does z go from 0 to ∞?" Your question is unclear, which is why no one will answer.

Generally, branch cuts can be made fairly arbitrarily as long as they make sense. Though, I personally prefer to use Riemann surfaces because they are more fun for me.

 

[Office_Shredder]

Certainly if you have a domain where ln(z) is defined holomorphically, then ln(z)² is also holomorphic on the same domain

 

[CrimsonFlash]

Ok thanks.