(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1. Find and isomorphism of the region [tex] |arg z|< \frac{\pi}{8} [/tex] on the region:

[tex] |z|<1,z Not In [0,1) [/tex].

2. Find and isomorphism of the region [tex]D= (z=i+re^{it}, \frac{5 \pi}{4} < t<\frac{7 \pi}{4}, r \geq 0 ) [/tex] on the region [tex] R=(z: 0<Rez< \pi , Imz>0) [/tex].

2. Relevant equations

Mobiuos Transformations...Elementry Functions

3. The attempt at a solution

I have no idea about 2...

About 1- I thought about first taking the function [tex] z \to z^8 [/tex] which will copy the region to [tex] C-(- \infty, 0] [/tex] ... I was thinking about using LOG or something from that point, but I have no idea how to continue this composition of functions

Hope you'll be able to help me

Thanks

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# Homework Help: Complex Analysis-Isomorphisms

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