Bilinear Transformation examples: Conformal Mapping lecture-10

#3 || Problem#1|| Bilinear transformation || 𝒛=𝟏, 𝒊, −𝟏 𝒂𝒏𝒅 𝝎=𝒊, 𝟎, −𝒊 || 18MAT41 ||

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every bilinear transformation maps circle or straight line into circle or straight line

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Find the Bilinear Transformation which maps the points z1=1, z2= i, z3=-2 to w1=1,w2=i, w3= -1

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Find Bilinear Transformation that maps the points 𝑧₁=∞, 𝑧₂= 𝑖, 𝑧₃=0 into the points 𝑤₁=0, 𝑤₂=𝑖, 𝑤₃=∞

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#4 || Problem#2 || Bilinear transformation || 𝒛=∞, 𝒊, 𝟎 𝐢𝐧𝐭𝐨 𝝎=−𝟏, −𝒊, 𝟏 || Fixed points ||