I'm taking a complex variables course, and I'm really stuck at it, I've never felt this way in any math course before :S, I'm starting to get angry. Anyway here is the problem, I hope someone can give me a hand. I believe this is a basic and simple problem in the subject...(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Let D be the domain obtained by deleting the ray {x:x[tex]\leq[/tex]0} from the plane, and let G(z) be a branch of log z on D. Show that G maps D onto a horizontal strip of width of 2[tex]pi[/tex]

{x+iy: -[tex]\infty[/tex]<x<[tex]\infty[/tex], c_{o}<y<c_{o}+2[tex]pi[/tex]},

and that the mapping is one-to-one on D.

2. Relevant equations

3. The attempt at a solution

Ok so first off I'm trying to actually understand the problem. Where it says deleting the ray {x:x[tex]\leq[/tex]0} I don't know exactly what it means. I mean, in my mind there is an infinite number of rays that satisfy those conditions (all the rays going from the imaginary axis and going left all the way to infinity, parallel to the x axis). I think I'm way off here, but believe me, I've read the textbook and it just isn't clear to me this all thing about rays and branches. Plus, I can't picture the branch of log z if I can't picture D in the first place! Could somebody help me with understanding this please?

Thanks a lot.

NOTE: The infinities are not supposed to be exponentials, I don't know why they appeared that way.

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# Homework Help: Complex variables: Logarithm function.

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