TT1 Problem 5 (morning)

[Victor Ivrii]

$\renewcommand{\Re}{\operatorname{Re}}
\renewcommand{\Im}{\operatorname{Im}}$
Find any region that is mapped bijectively to $\{w\colon \Re w\ge |\Im w |, \ 0< |w|\le 2\}$ by the map $w=e^z$. Draw both of them.

[Xiting Kuang]

Please see the solution below.

[Xiting Kuang]

Corrections done above.

[Xiting Kuang]

Corrections done above.

[Victor Ivrii]

You can modify your post and remove unwanted attachments. What are domains (you draw several), which one is correct? You need to state it explicitly rather than leaving to guesses.

Also, use LaTeX/MathJax instead of pitiful html math (or mess)

[Victor Ivrii]

You need to say that domains in both cases are intersections of the "painted" domains.