Fixed Points and Normal form of Bilinear Transformation of w = z-1/z+1

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Find the Fixed Points and Normal Form of Bilinear Transformation of w = 3z-4/z-1 CONFORMAL MAPPINGFind the Fixed Points and Normal Form of Bilinear Transformation of w = 3z-4/z-1 CONFORMAL MAPPING
Every Bilinear Transform with one fixed point 𝑝 can be put in 1/(𝑀-𝑝)=π‘˜+{1/(𝑧-𝑝)} where π‘˜=π‘Ž/(π‘Ž-𝑐𝑝).Every Bilinear Transform with one fixed point 𝑝 can be put in 1/(𝑀-𝑝)=π‘˜+{1/(𝑧-𝑝)} where π‘˜=π‘Ž/(π‘Ž-𝑐𝑝).
find fixed point and normal form of the bilinear transactionfind fixed point and normal form of the bilinear transaction
Invariant points of the bilinear transformation w=(1+z)/(1-z)###fixed points///invariant points///Invariant points of the bilinear transformation w=(1+z)/(1-z)###fixed points///invariant points///
Bilinear Transformation (0,1,∞) into (-1,-i,1) and (0,1,∞) into (-1,-2,-i)Bilinear Transformation (0,1,∞) into (-1,-i,1) and (0,1,∞) into (-1,-2,-i)
Normal form of bilinear transformation with one fixed pointNormal form of bilinear transformation with one fixed point
State & proof Normal form of Bilinear Transformation: (𝑀-𝑝)/(𝑀-π‘ž)=π‘˜(𝑧-𝑝)/(𝑧-π‘ž) whereπ‘˜=(π‘Ž-𝑐𝑝)/(π‘Ž-π‘π‘ž)State & proof Normal form of Bilinear Transformation: (𝑀-𝑝)/(𝑀-π‘ž)=π‘˜(𝑧-𝑝)/(𝑧-π‘ž) whereπ‘˜=(π‘Ž-𝑐𝑝)/(π‘Ž-π‘π‘ž)
For z = 1 as the only invariant point, Bilinear Transf. can be put in the form 1/w-1 = 1/z-1 + 1/kFor z = 1 as the only invariant point, Bilinear Transf. can be put in the form 1/w-1 = 1/z-1 + 1/k