As an aside, I'm also struggling with lim(z-->-1)
My initial feeling was non-existance, but now Im not sure
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?
Thanks in advanced,