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

A rotation preserves norms but changes arguments:

This is shown with the polar form of z, z = re

f(z) = e

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

- Ex.1

Draw a horizontal line in the domain. What happens in the image? Explain.

- Ex.2

Draw a square in the domain. How has it changed in the image?

- Ex.3

Draw a circle in the domain. How has it changed in the image?

- Ex.4

Draw a square in the image. How has it changed in the domain?

Using the applet.

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