b)  Show that there is only one linear fractional transformation that maps three given distinct points z₁,z₂ and z₃ in the extended z plane onto three specified distinct pointsw₁ ,w₂ and w₃   in the extended w plane.

To show that there is only one linear fractional transformation that maps three given distinct points z1, z2, and z3 in the extended z-plane onto three specified distinct points w1, w2, and w3 in the extended w-plane, we will first find the general form of a linear fractional transformation, and then show that it is uniquely determined by the given points.

A linear fractional transformation (LFT), also known as a Möbius transformation, is a function of the form:

f(z) = (az + b) / (cz + d)

where a, b, c, and d are complex __________ ________ ______ ___ _____.
______ ________ ___ _______ _________ __________ _____ ________ ______ ____.
_________ ___ _________ _______ _____ ______ ____.
_____ ____ _______ _________ _______ ________ __________ ___ ____.
____ ___ ____ ______ ______ ______ ___ _________ ____ _________.
__________ _________ __________ ________ _________ ___ ___ ____ ________ __________ ____ ____.
_____ _________ ____ _______ _______ ________ ___ _____ _____.
___ _____ ______ ____ ____ __________ ___ _____ ______ __________ ___ ___.
________ _________ ______ ________ _________.
____ ______ _____ _____ _____ ______.
____ ___ ________ ___ _________ ___ _________ _______ ____.
_______ _________ ______ ________ ________ ____ ______ __________ ____ _______.
________ ________ ________ _________ __________ ___ ____ _________.
___ _______ ______ ________ ______ ______ ___ ___ _________ ___ ___.
___ ____ ______ ________ _____ ________ ______.
____ ____ __________ __________ ___ ___ _________ _______ ____.
________ ___ _________ ______ _________ ___ ________ ____ ____ _______ _______.
____ _____ _________ _____ ______ _____ _______ ______ _______.
_________ _________ ___ ______ __________ ___ ___ ____ ___.
______ _____ ________ __________ _____ _________ ________ _____ ______ _________ _________ _________.
______ ___ _________ ______ ____ ____.
__________ ___ _________ ___ _________ ___ _____ _________ __________ _______.
_______ ____ _________ _____ ___ _________ _______ __________.
___ ______ _____ __________ ___ ________ _____ ___ __________ ___.
____ _____ _________ ________ ___.
________ ________ _________ _____ _____ ___.
_____ _____ ______ _________ ________ _____.
_____ ___ _____ __________ ___ ___ ________ _______ ________ _____ _____ _______.
_______ _______ __________ ________ ______ ________ _____ _____ ______ ________.
_________ __________ _______ ___ _________.
____ ____ ____ _________ ____ _____ ____ _______ _______ ____.
___ ___ _____ _____ _________ ___ ______ _____ _______ _________ _________ ____.
_________ ____ ____ _________ ________ ________ _____ _________ _________ __________ _____.
_________ ___ ______ _____ ________ _____ _________ ________.
_____ ________ ________ _______ ___ ________ _____ _____ _______ ____ ______ ______.
___ ___ _____ __________ _______ __________ _________ ____ _____.
_____ _______ _________ ______ ________ _______ _________ ___.
____ __________ ___ ___ ____.
____ ________ ________ ________ ____ __________ ____ ________ _________ ______ _________.
______ ___ __________ ________ ________ _________ ____ _______.
__________ _____ _______ __________ __________ ______.
___ ______ __________ _______ _______ _______ _____ _________ _________ _______.
_______ __________ ____ ______ ____ __________ _____ ________ _____ ____.
__________ _______ _______ _______ ________ ________ _____ ____.
___ ____ _____ _______ __________ ____ ____.
___ _______ _____ __________ _________.
___ _______ _________ ____ ______ __________ __________ _________ ___.
______ ________ _______ ______ ___ ___ _______ ________.
______ ______ _________ ________ _______ _____ ______ _________ ______.
________ _______ _____ ___ _________ _____ ____ ______.
Get Full Answer on WhatsApp