Where Does the Branch Cut of Log(z^2+9) Lie?

[FunkyDwarf]

Hey guys,

I need to find the branch cut of the function f(z) = Log[z^2 +9] where the negative real axis has been removed from the domain of the log function. Now this is the bit that confuses me, is this saying that we must ensure that no negative real components enter the argument of the log function or is it saying theyre not part of the domain don't worry about them?

Anyway, i factor it out and you get f(z) = log(z+3i)+log(z-3i). My understanding is the branch cut is the line segment(s) on which the function is discontinuous, so are we just saying that the imaginary part of z must be >3i or <-3i ? I'm a bit confoosed =(

Cheers
-G

 

[benorin]

The angle the branch cut makes with the negative real axis is not always 0, is it plum?

 

[Avodyne]

I need to find the branch cut of the function f(z) = Log[z^2 +9] where the negative real axis has been removed from the domain of the log function. Now this is the bit that confuses me, is this saying that we must ensure that no negative real components enter the argument of the log function

No

or is it saying theyre not part of the domain don't worry about them?

Yes. So, this means that the branch cut of log(z) lies on the negative real axis. And that means that the branch cut of log(z^2+9) lies ... where?