This online resource is based on a preparatory course "Mathematics for Engineering" at the International College of the University of Applied Sciences Kaiserslautern in summer term 2009. Its purpose is to make students familiar with the basic principles of complex numbers. Combining explanatory text, exercises and interactive GeoGebra applets, this resource is suitable for both classroom lectures and distance learning. The text and the exercises are available as html format (Firefox recommended) or as printable pdf-files. Before dealing with this resource efficiently, students should have gained basic knowledge of numerical algebra and vector algebra.

This online resource is based on a preparatory course "Mathematics for Engineering" at the International College of the University of Applied Sciences Kaiserslautern in summer term 2009. Its purpose is to make students familiar with the basic principles of complex numbers. Combining explanatory text, exercises and interactive GeoGebra applets, this resource is suitable for both classroom lectures and distance learning. The text and the exercises are available as html format (Firefox recommended) or as printable pdf-files. Before dealing with this resource efficiently, students should have gained basic knowledge of numerical algebra and vector algebra.

The Basic Calculations Applet allows users to input complex numbers in either cartesian or exponential form and display them in vector form. The applet also shows the results of conjugation and basic arithmetic of complex numbers.

Open the Basic Calculations Applet in a new browser window

Using the Basic Calculations Applet:

The activities below lead the reader through basic concepts, definitions and properties of the complex numbers using the Basic Calculations applet.

The Exponentiations Applet allows users to input complex numbers in either cartesian or exponential form and display them in vector form. The applet also shows the results of applying powers and roots to complex numbers. The applet, constructed using GeoGebra, requires Java 1.4.2 or later.

Open the Exponentiations Applet in a new browser window

Using the Exponentiations Applet:

The activity below leads the reader through additional concepts, definitions and properties of the complex numbers using the Exponentiation applet.