Hi guys I need some help with this homework question!
Find a bilinear transformation $w = f(z)$ which maps the line $\{\Re z = 0\}$ to the circle $\{|w|=1\}$ and $\{\Re z > 0\}$ to $\{|w|< 1\}$.
Hence find a bilinear transformation $w = g(z)$ which maps the line $\{\Im z =\Re z\}$ to the circle $\{|w+i| = 1\}$ and $\{\Im z <\Re z\}$ to $\{|w+i| < 1\}$.