• 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