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Complex Powers of e

Contents 1 Complex Powers of e 1.1 Image of a Vertical Line 1.2 Image of a Horizontal Line 1.3 Image of an Arbitrary Line

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.