Differential Equations

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

Read the course notes:

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

Watch the lecture video clip:

• Justification of Euler’s Formula

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

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

Read the course notes:

• Finding n-th Roots (PDF)

Watch the lecture video clip:

• Nth Roots

Watch the problem solving video:

• Complex Numbers and Euler’s Formula

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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