Lesson Worksheet: Möbius Transformations Mathematics
In this worksheet, we will practice interpreting möbius transformation in the complex plane.
Q1:
Consider the MΓΆbius transformations and , where or 0.
Write an expression for the composition .
- A
- B
- C
- D
- E
Q2:
A transformation that maps the -plane to the -plane is defined by , where .
Find an equation for the image of under the transformation.
- A
- B
- C
- D
- E
Find an equation for the image of .
- A
- B
- C
- D
- E
Find a Cartesian equation for the image of .
- A
- B
- C
- D
- E
Find a Cartesian equation for the image of .
- A
- B
- C
- D
- E
Q3:
A transformation that maps the -plane to the -plane is defined by .
Find the Cartesian equation for the image of .
- A
- B
- C
- D
- E
Find the Cartesian equation for the image of .
- A
- B
- C
- D
- E
Q4:
Which of the following MΓΆbius transformations maps to the real axis?
- A
- B
- C
- D
- E
Q5:
A transformation, , that maps the -plane to the -plane is given by , where .
Find a Cartesian equation for the image of the imaginary axis under the transformation .
- A
- B
- C
- D
- E
Hence, find the image of the region under the transformation .
- A
- B
- C
- D
- E
Q6:
Suppose is a linear transformation with . What is the value of ?
- A
- BThis depends on the definition of .
- C1
- D
- E7
Q7:
Suppose is a linear transformation. What is the value of ?
Q8:
Which of the following MΓΆbius transformations, , maps to 0, 0 to , and has ?
- A
- B
- C
- D
- E
Q9:
Find the equation for the image of under the transformation , , which maps the -plane to the -plane.
- A
- B
- C
- D
- E
Q10:
A transformation, , that maps the -plane to the -plane is given by , where . Find the image of the region under the transformation .
- A
- B
- C
- D
- E
Practice Means Progress
Boost your grades with free daily practice questions. Download Nagwa Practice today!
