10.5.47 Conformal mappings
Condition: Find the image of the region \( D=\left\{-\frac{3 \pi}{2}<\operatorname{Im} z<\frac{\pi}{2}\right\} \backslash \) \( \left\{z=i t, t \in\left[0, \frac{\pi}{2}\right)\right\} \) when displaying \( f(z)=e^{-\frac{z}{2}} \).
Problems of finding conformal mappings of domains with and without cuts, using linear fractional functions, trigonometric functions, power functions, Zhukovsky function.