10.5.49 Conformal mappings
condition: Find the image of the region \( D=\left\{0<\operatorname{Re} z<\frac{\pi}{4}\right\} \) under the mapping \( f(z)=\cot z \).
Problems of finding conformal mappings of domains with and without cuts, using linear fractional functions, trigonometric functions, power functions, Zhukovsky function.