Find the bilinear transformation which maps the points
z =1,i,-1
into the points
w =0,1,infinity
respectively. What are the invariant points under this transformation?
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Answer:
sorry did not understand your question pl explain properly
Answered by
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ans:-
(w-w1) (w2-w3)/(w-w3)(w2-w3)=(z-z1) (z2-z3)/(z-z3) (z2-z1)
w/-1= (z-1) (i+1)/(z+1) (i-1) * 1/-1
-w = (z-1)/z+1 [i+1 /-i+1]
w=-(z-1)/(z+1)[i+1)/(1-i) * (1+i)/(1+i)
w= -(z-1)/z+1 [(i=+1)^2/ 1^2-i^2
w=-(z-1)/(z+1)[ i^2+1^2+2i/(1-(-1))]
w= -(z-1)/(z+1)[2i/2]
w= i(1-z)/(z+1)
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