Complex Arithmetic and Exponentials

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Session Overview

In this session we will learn complex arithmetic and Euler's formula. These are important algebraic tools used throughout the course.

Session Activities

Read the course notes:

• Complex Arithmetic and Exponentials: Introduction (PDF)
• Complex Arithmetic (PDF)

Watch the lecture video clip:

• Complex Arithmetic, Euler's Formula (00:06:37)

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  Complex Arithmetic, Euler's Formula (00:06:37)

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• Transcript (PDF)

Read the course notes:

• Complex Arithmetic Examples (PDF)
• Euler's Formula, Polar Representation (PDF)

Watch the lecture video clip:

• Justification of Euler's Formula (00:17:21)

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  Justification of Euler's Formula (00:17:21)

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• Transcript (PDF)

Check Yourself

Take the quizzes:

• Multiplication by i (PDF)
• Choices (PDF)
• Answer (PDF)


• Complex Conjugation (PDF)
• Choices (PDF)
• Answer (PDF)


• Complex Powers (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Read the course notes:

• Complex Exponentials (PDF)

Watch the lecture video clip:

• Polar Form (00:06:02)

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  Polar Form (00:06:02)

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• Transcript (PDF)

Learn from the Mathlet materials:

• Read about how to work with the Complex Exponential Applet (PDF)
• Work with the Complex Exponential Applet

Check Yourself

• Complex Exponentials (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Watch the lecture video clip:

• Example: Complex Replacement (00:09:35)

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  Example: Complex Replacement (00:09:35)

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• Transcript (PDF)

Read the course notes:

• Finding n-th Roots (PDF)

Watch the lecture video clip:

• Nth Roots (00:05:53)

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  Nth Roots (00:05:53)

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• Transcript (PDF)

Watch the problem solving video:

• Complex Numbers and Euler's Formula (00:11:29)

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  Complex Numbers and Euler's Formula (00:11:29)

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• Transcript (PDF)

Complete the practice problems:

• Practice Problems 6 (PDF)
• Practice Problems 6 Solutions (PDF)

Check Yourself

Complete the problem sets:

• Problem Set Part I Problems (PDF)
• Problem Set Part I Solutions (PDF)


• Problem Set Part II Problems (PDF)
• Problem Set Part II Solutions (PDF)

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