Rotation Maps

A rotation map is a conformal map of the form f(z) = e^iθz.

A rotation preserves norms but changes arguments:
This is shown with the polar form of z, z = re^iα.

f(z) = e^iθz = e^iθre^iα = re^i(θ+α)

⇒ the norm is preserved, namely r, but the argument is increased by the rotation angle, θ.

Use the rockin' applet below to do the following exercises:

1. Ex.1
   Draw a horizontal line in the domain. What happens in the image? Explain.
   
   
2. Ex.2
   Draw a square in the domain. How has it changed in the image?
   
   
3. Ex.3
   Draw a circle in the domain. How has it changed in the image?
   
   
4. Ex.4
   Draw a square in the image. How has it changed in the domain?
   
   
   
   Using the applet.
   
   
   
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