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Conformal Mappings

Let O be the upper half of the unit disc D. Find a conformal mapping f: O->D that maps {-1,0,1} to {-1,-i,1}.

Find z in O with f(z)=0

Solution Preview

We consider the mobius transformation f(z)=(az+b)/(cz+d).
Since f maps {-1,0,1} to {-1,-i,1}, then
(1) f(-1)=(-a+b)/(-c+d)=-1 => -a+b=c-d
(2) f(0)=b/d=-i ...

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Conformal mappings are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.