Let T( z ) = (az+b)/(cz+d)
Find a, b, c, d in ℂ with T( 0 ) = -0.5 - 1.5i, T( 1 ) = 3 + 4.5i and T( ∞ ) = 1.5 - 2.5i
Hey,guys.This is last question of my exercise and this is due 8 hours later.I can't solve it and I think it has no solution.Someone please give this a try.Thank you in advance. Basically, you get 3 equation: b/d=-0.5-1.5i (a+b)/(c+d)=3+4.5i, a/c =1.5-2.5i and solve the system of equation for a,b,c,d with some complex number trick.
See chapter 3 section 1 and section 2 of the following book for reference.
See you guys later.
I found the answer with wolframalpha,simply enter these b/d=-0.5-1.5i , (a+b)/(c+d)=3+4.5i, a/c =1.5-2.5i to wolframalpha to get the answer.However, I still encourage you to give this a try by yourself.