GeoGebra

Complex Powers of e

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Complex Powers of e

The following files illustrate the images of various lines under f(z) = ez.

This complex mapping is a combination of a dilation and a rotation. If z is looked at as an ordered pair (xz,yz), then f(z) = ez takes the point (1,0), dilates it by a factor of e^{x_z}, and rotates it by yz radians about the origin.

All these files have a Complex Powers of e tool.

Image of a Vertical Line

This file illustrates the Ggb.gifImage of a Vertical Line under the complex mapping f(z) = ez.

Image of a Horizontal Line

This file illustrates the Ggb.gifImage of a Horizontal Line under the complex mapping f(z) = ez.

Image of an Arbitrary Line

This file illustrates the Ggb.gifImage of an Arbitrary Line under the complex mapping f(z) = ez.