13. Conformal Mapping

Mapping Regions — Quiz

Test your understanding of mapping regions with 5 practice questions.

Practice Questions

Question 1

What is the image of the strip $\{z:-1<\Re z<1\}$ under the map $w=z+2$?

Question 2

What is the image of the first quadrant $\{z:\Re z>0,\Im z>0\}$ under the map $w=z^2$?

Question 3

What is the image of the strip $\{z:0<\Im z<\pi\}$ under the map $w=e^z$?

Question 4

What is the image of the unit disk $\{z:|z|<1\}$ under the map $w=\frac{1+z}{1-z}$?

Question 5

What is the image of the upper half-plane $\{z:\Im z>0\}$ under the map $w=\frac{z-i}{z+i}$?