Complex Variables: Numerical & Basic Concepts of Bilinear (Mobius) Transformation

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

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

Prove that the cross ratio remains invariant under a Bilinear Transformation.Подробнее

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Find the image of the circle |𝑧-2|=2 under the Mobius transformation 𝑤=𝑧/(𝑧+1) .Подробнее

Find the image of the circle |𝑧-2|=2 under the Mobius transformation 𝑤=𝑧/(𝑧+1) .

Find all Mobius (Bilinear) Transformations which transform unit circle |𝑧|≤1 into unit circles |𝑤|≤1Подробнее

Find all Mobius (Bilinear) Transformations which transform unit circle |𝑧|≤1 into unit circles |𝑤|≤1

Find all Mobius ( Bilinear) Transformations which transform half plane 𝐼(𝑧)≥0 into circles |𝑤|≤1 .Подробнее

Find all Mobius ( Bilinear) Transformations which transform half plane 𝐼(𝑧)≥0 into circles |𝑤|≤1 .

Prove every Bilinear Transformation map circles or straight lines into circles or straight lines.Подробнее

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Prove the resultant (or product) of two Bilinear Transformation is also a Bilinear Transformation.Подробнее

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"Bilinear Transformation" as a combination of the transformation, rotation, stretching & Inversion.Подробнее

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