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## Complex Powers of e

## Contents |

# Complex Powers of e

The following files illustrate the images of various lines under *f*(*z*) = *e*^{z}.

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

All these files have a Complex Powers of e tool.

#### Image of a Vertical Line

This file illustrates the Image of a Vertical Line under the complex mapping *f*(*z*) = *e*^{z}.

#### Image of a Horizontal Line

This file illustrates the Image of a Horizontal Line under the complex mapping *f*(*z*) = *e*^{z}.

#### Image of an Arbitrary Line

This file illustrates the Image of an Arbitrary Line under the complex mapping *f*(*z*) = *e*^{z}.