Question

Find a linear fractional transformation that carries the circle onto the line .

Answer 1

am very close to the solution I think. Since the circles cross the real axis, I want to find mappings from z→wz→w such that 1/2→m1/2→m and 0→−m0→−mand −1→n−1→n and 1→−n1→−n. Using

w=az+bcz+dw=az+bcz+d

we get

a+2bc+2d=−bda+2bc+2d=−bd

and

b−ad−c=−a+bc+db−ad−c=−a+bc+d

but where do we go from here? I am a little lost in the simplifying algebra here to solve for the a,b,c,da,b,c,d in the transformation.