Rotation Maps


A rotation map is a conformal map of the form f(z) = ez.

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

f(z) = ez = ere = rei(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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