Find a conformal map
from \(\{ z : | z - 1 / 2 | > 1 / 2 , { \mathrm { R e } } ( z ) > 0 \}\) to H
from \(\left\{ z : | z - 1 / 2 | > 1 / 2 , | z | < 1 \right\}\) to D
from the intersection of the disk \(| z + i | < { \sqrt { 2 } }\) with H to D.
from \(\mathbb { D } \backslash [ a , 1 )\) to \({ \mathbb D } \backslash [ 0 , 1 ) ~ ( 0 < a < 1 )\) . Short solution possible using Blaschke factor
from \(\{ z : | z | < 1 , \mathrm { R e } ( z ) > 0 \} \backslash ( 0 , 1 / 2 ]\) to H.