# Thread: Complex Limit Question (Log)

1. ## Complex Limit Question (Log)

Hey guys,

I'm having trouble trying to PROVE why the lim z-->0 of Log(z) = infinity

What I've done (doesnt look right, obviously, else I wouldnt post!) is the following:-

Log(z) = ln|z| + iArg(z)

|z| = 0
arg(0) = 0

Log(z) = ln(0)

But. My arguement now is that as z-->0, ln|z| will APPROACH negative infinity, but (recalling a priniciple mentioned in class) the complex plane only has "infinity" not plus/minus inf, so that goes to "infinity"

As I said, this looks like a terrible argument. Can someone please clarify/assst with the proof plz?

XPhaTe

2. As an aside, I'm also struggling with lim(z-->-1)

My initial feeling was non-existance, but now Im not sure

3. Originally Posted by exphate
As an aside, I'm also struggling with lim(z-->-1)

My initial feeling was non-existance, but now Im not sure

Originally Posted by exphate
Hey guys,

I'm having trouble trying to PROVE why the lim z-->0 of Log(z) = infinity

What I've done (doesnt look right, obviously, else I wouldnt post!) is the following:-

Log(z) = ln|z| + iArg(z)

|z| = 0
arg(0) = 0

Log(z) = ln(0)

But. My arguement now is that as z-->0, ln|z| will APPROACH negative infinity, but (recalling a priniciple mentioned in class) the complex plane only has "infinity" not plus/minus inf, so that goes to "infinity"

As I said, this looks like a terrible argument. Can someone please clarify/assst with the proof plz?

XPhaTe
Note that z = 0 is a branch point.