About This Chapter
Geometric Representations of Complex Numbers - Chapter Summary
Our instructors present the geometric representations of complex numbers in this chapter. The informative lessons provided here explain the definition of a modulus of a complex number and the argument of complex numbers. You'll also learn about using Argand diagrams to represent complex numbers. After completing this chapter, you should be able to:
- Explain complex numbers as vectors
- Use complex numbers to construct vectors
- Understand geometric proofs that show complex numbers as vectors
Even the toughest subjects are simple to understand with help from our professionally designed lessons. Each one is followed by a multiple-choice quiz that you can use to test your understanding of what you've learned. You're welcome to access these materials at any time on your mobile phone, tablet or computer. Just reach out to an instructor if need any assistance as you work through the chapter.
1. Modulus of a Complex Number: Definition & Examples
In this lesson, we will explore complex numbers and an important characteristic of these numbers called a modulus. We will look at what a modulus of a complex number is, how it relates to other aspects of a complex number, and how to find it.
2. Argument of Complex Numbers
Read this lesson to learn how trigonometry and the complex plane are used to find the argument of a complex number. You will also learn how to pair an angle with the corresponding argument.
3. Representing Complex Numbers with Argand Diagrams
Complex numbers are used throughout math, science and engineering. This lesson uses examples to show how to represent a complex number with Argand diagrams.
4. Complex Numbers as Vectors
In this lesson, you'll learn how you can work with complex numbers as vectors. You'll learn how to find the magnitude of these vectors as well as how the argument of the vector relates to the vector's angle.
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Other chapters within the HSC Mathematics: Exam Prep & Syllabus course
- Mathematical Proofs & Reasoning
- Basic Arithmetic & Algebra
- Factorization of Binomials & Trinomials
- Types of Equations & Inequalities
- Plane Geometry
- Circle Plane Geometry
- Probability & Randomization
- Arithmetic & Geometric Series
- Trigonometric Ratios
- Geometrical Representations of Functions
- Linear Functions & Lines
- Derivatives of Functions
- Quadratic Polynomials & Parabolas
- Geometrical Applications of Differentiation
- Logarithmic & Exponential Functions
- Calculating Trigonometric Functions
- Understanding Inverse Functions
- Factoring & Graphing Polynomials
- Roots & Coefficients of Polynomials
- Binomial Theorem & Probability
- Graphing & Solving Functions
- Solving & Graphing Complex Numbers
- Square Roots, Powers & Roots of Complex Numbers
- Conic Sections Basics
- The Ellipse in Algebra
- The Hyperbola
- The Rectangular Hyperbola
- Calculus Applications: Rate of Change
- Calculus Applications: Velocity & Acceleration
- Calculus Applications: Projectile & Harmonic Motion
- Calculus Applications: Resisted Motion
- Calculus Applications: Circular Motion
- HSC Mathematics Flashcards