10.5.11 Conformal mappings

Problem: Find the image of domain \( D \) for the mapping \( w=f(z) \), where \[ D:\left\{\begin{array}{c} 0<\operatorname{Re} z<\frac{1}{2}, \quad f(z)=\tan \pi z . \\ \operatorname{Im} z>0 \end{array}\right. \]