Answer to Question #1907 in Complex Analysis for SAVVAS SAVVAN
Could someone shine some light on how to find the inverse,the domain and the rule of the
f(z)= ln [(z+1+i)/3]
Similar to the functions of real variable. The inverse function to logariphm is exponenta: ln [(z+1+i)/3] = ln (z+a) - ln3, where a = 1+i. ln(f(z)+a) - ln3 = z f(z)+a = e(z+ln3) f(z) = e(z+ln3) - a = 3ez -a Thus inverse is 3ez-1-i. The domain is z+a > 0, z > -a, z > (1+i).