Day 5 in Mat430

Today:

• Announcements
  • Today's activity, and new assignment:

    Fri

    1/22

    Sections 6,7

    Read Section 8 (from handout)

• Sections 5 and 6: polar and exponential forms
  • Now we'll introduce the notion of representing complex numbers using a polar representation.
    • the non-uniqueness of zero....
    • Arg versus arg (principal value)
    • An interesting discovery about products and their arguments....
  • Section 6: There's an interesting relationship that arises between exponential and trigonometric functions....
    • Euler's formula
    • Euler's formula can be derived nicely using Taylor Series expansions
    • This representation enables us to do some nice things in computer graphics easily!

• Section 7: Powers and roots
  • Roots of Unity
  • de Moivre's formula
  • More graphics: graphing regular polygons
  • Principal roots