Complex Numbers
Complex number arithmetic, modulus-argument form, Argand diagram geometry, polar form with De Moivre's theorem, roots of unity, and complex polynomials.
Active lessons
6
Status
Active
Lesson flow
Learn -> Guided Practice -> Independent Practice -> Mastery Quiz
How to use this unit
- Start from lesson 1 and move through the pathway in order.
- Use guided practice before attempting independent practice.
- Mastery quizzes check whether the skill is ready for review or extension.
Unit pathway
Lesson pathway
6 of 6 active
Lesson 1
Complex Number Arithmetic
Practise complex number arithmetic with concise examples and mastery checks.
Lesson 2
Modulus, Argument and Conjugate
Practise modulus, argument and conjugate with concise examples and mastery checks.
Lesson 3
Argand Diagram and Geometry
Practise argand diagram and geometry with concise examples and mastery checks.
Lesson 4
Polar Form and De Moivre's Theorem
Practise polar form and de moivre's theorem with concise examples and mastery checks.
Lesson 5
Roots of Unity
Find all nth roots of unity using De Moivre's theorem, plot them on the Argand diagram as equally-spaced points on the unit circle, and prove their sum is zero.
Lesson 6
Complex Polynomials
Apply the conjugate root theorem to real polynomials, find complex roots in conjugate pairs, and factorise real polynomials over ℂ into linear and irreducible quadratic factors.
Part of the Online Learning Package
Unit previews stay public, while individual lessons require active online learning access.