Mobius transformation :
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   Substituting the values of $z_{1}$, $z_{2}$, $z_{3}$, $w_{1}$, $w_{2}$ and $w_{3}$, we get MATH
 Therefore, the required Mobius transformation is MATH
.
Example 2: Find the Mobius transformation that maps $0$, $1$, $\infty$ to $1$, $i$, $-i$ respectively.
Set $z_{1} = 0$, $z_{2} = 1$, $z_{3} = \infty$, $w_{1} = 1$, $w_{2} = i$, $w_{3} = -1$. To find the Mobius transformation $w = T(z)$ such that $T(z_{i}) = w_{i}$ for $i=1$, $2$, $3$, We use the following formula MATH
 
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