1. The problem statement, all variables and given/known data Find the bilinear transformation that maps the points z1=infinity, z2=i, z3=0 to the points w1=0, w2=i, w3=infinity. 2. Relevant equations w=(az+b)/(cz+d) The answer is -1/z 3. The attempt at a solution We have: infinity --> 0 i --> i 0 --> infinity Since 0 goes to infinity, it means the denominator "is 0", so therefore d must be 0 in our relevant equation right off the bat. If we take the limit as z--> infinity, we are supposed to get w=0, so 0=a/c in the limit and we see that a=0. So now we are left with b/cz and i--> i=b/(ci) and we see that -c=b But how do I prove here that c=1, and b=-1 instead of something else? thanks.