Mobius transformation :
Print this page
  
 
First   |   Last   |   Prev   |   Next
  


Similarly, it maps the lower half plane MATH onto $\vert w \vert > 1$. Further, any pair of points symmetric with respect to the real axis $L$ are mapped by $T$ onto a pair of points symmetric with respect to the unit circle $C$.

Example 3: Find the bilinear transformation which takes the points $-1$, $\infty$, $i$ into the points $\infty$, $i$, $1$.
Answer: MATH.

Example 4: Find the most general bilinear transformation which maps the upper half plane $\Im(z) > 0$ of the $z$-plane onto the unit open disk $\vert w \vert < 1$. Answer: MATH where $\theta$ is a real constant and $\alpha$ is a complex constant with $\Im(\alpha)>0$.

Example 5: Find all Mobius transformations that map $\vert z \vert < 1$ onto $\vert w \vert < 1$.
Answer: MATH where $\theta$ is a real constant and $\alpha$ is a complex constant with MATH.

 
First   |   Last   |   Prev   |   Next