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avatar+575 

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.

http://facstaff.cbu.edu/~yanushka/ca/beckL.pdf

See you guys later.

fiora  Oct 5, 2018
 #1
avatar+575 
+2

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.

fiora  Oct 5, 2018
 #2
avatar+94181 
+1

Hi Fiora,

I did look at your question but it was bejond me. :(

Melody  Oct 7, 2018

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