10.5.16 Conformal mappings

Problem: Find the image of domain \( D \) for the mapping \( w=f(z) \), where \[ D:\left\{\begin{array}{l} \operatorname{Re} z<0 \\ |\operatorname{Im} z|<\frac{\pi}{4}, \quad f(z)=\operatorname{th} 2 z . \end{array}\right. \]