Supercazzola Posted April 27 Share Posted April 27 (edited) Show how to get a conformal map from the region outside a semicircle, C∖SR={(x1,x2):|x1|2+|x2|2=R2,x2≤0} to the region outside a disk D of radius R2–√ centered at the origin, C∖D , ending up with h(u)=iR+u+i⋅R2−u2−−−−−−−√2 , with u=x1+ix2 . I know that the idea is to use a Moebius transform to send the semicircle to two perpendicular lines through the origin (something like az+Rz−R ) keeping track where infinity goes, then compress the three quarters we get the outside sent too to a half plane (again keeping track of infinity), then send that to the unit circle with infinity to 0 and then invert with z→c/z to get the outside circle of right radius and send infinity back to itself, but I didn't manage to get the correct result. Could you help me? Edited April 27 by Supercazzola Link to comment Share on other sites More sharing options...
Supercazzola Posted May 1 Author Share Posted May 1 Someone to help me? Link to comment Share on other sites More sharing options...
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