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

Let z = re

Thus angles are multiplied by p, and norms are raised to the p power.

Our applet considers the case when p = 2 (quadratic).

Recall that f(z) = z

Please draw slowly across the branch cut in the quadratic grid!

- Ex.1

Draw a circle in the domain. How does it look in the image?

- Ex.2

Draw a ray in the domain. How does it look in the image?

- Ex.3

Draw a path in the left half plane of the domain. Trace its image, with a different color. What happens, and why?

Using the applet.

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