Question

find the transformation of Fixed points of
W = Z-1/
Z+1​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{w=\dfrac{z-1}{z+1}}$

$\underline{\textbf{To find:}}$

$\textsf{Fixed points of the given transformation}$

$\underline{\textbf{Solution:}}$

$\textsf{Fixed points are obtained by solving}$

$\textsf{the equation w(z)=z}$

$\implies\mathsf{\dfrac{z-1}{z+1}=z}$

$\implies\mathsf{z-1=z(z+1)}$

$\implies\mathsf{z-1=z^2+z}$

$\implies\mathsf{-1=z^2}$

$\implies\mathsf{z^2=i^2}$

$\implies\boxed{\mathsf{z=\pm\,i}}$

$\underline{\textbf{Answer:}}$

$\textbf{Fixed points are i and -i}$

$\underline{\textbf{Find more:}}$

Answer 2

Answer:

Step-by-step explanation: