• Chapter 16 – Complex Numbers

When students have completed this lesson they should be able to:

• Understand that new number systems can be created, provided that the definitions are algebraically consistent
• Appreciate that complex number algebra excludes inequalities
• Do calculations with complex numbers
• Know the meaning of conjugate complex numbers, and that non-real roots of equations with real coefficients occur in conjugate pairs
• Know how to represent complex numbers as translations or as points
• Know the meaning of modulus, and be able to use it algebraically
• Use complex numbers to prove geometrical results
• Solve simple equations with complex coefficients

Chapter 17 – Complex Numbers in Polar Form

When students have completed this lesson they should be able to:

• Know the meaning of the argument of a complex number
• Multiply and divide complex numbers in modulus-argument form
• Know how to represent multiplication and division geometrically
• Solve geometrical problems involving angles using complex numbers
• Write square roots in modulus-argument form
• Know that complex numbers can be written as exponentials