10.5.48 Conformal mappings
Condition: Find the image of the area \[ \begin{array}{l} D=\{\operatorname{Rez}>0\} \cup\{-2 \pi<\operatorname{Im} z<0\} \backslash\{z=t-\pi i, \\ t \in[0 ; 1]\} \text { when displaying } f(z)=\cos \frac{i t}{2} . \end{array}\]
Problems of finding conformal mappings of domains with and without cuts, using linear fractional functions, trigonometric functions, power functions, Zhukovsky function.