Day 4 in Mat430

Today:

• Announcements
  • I hope that all went well with you and Don Krug last time, and that you had a nice MLK holiday.
  • How's the book search going? Anyone else get an 8th edition?
  • Problem set #1 is due today.... How did that go?
  • Today's activity, and new assignment:

    Wed

    1/20

    Sections 5,6

    Read Section 7 (from handout); pp. 20--, #1b, 2b, 3c, 4, 6, 14, 17, 18, 19 (due Friday, 1/29)

• My understanding is that you did manage to cover Sections 3 and 4: geometric interpretation of complex numbers.
  • Complex numbers as ordered pairs suggest intepreting complex numbers as vectors.
    • Sums and differences using the parallelogram rule
    • Modulus == norm
    • Complex conjugate (already introduced via the quadratic equation)
    • Triangle inequality, and its interpretation and variations
  • Example problems to choose from:
    • 1cd -- simple example of manipulation
    • 6a -- the conjugate
    • 12 -- Using inequalities
    • 15b -- induction proof, property of conjugates
    • 18 -- equation of an hyperbola, conjugates
    • 19b -- interesting representation of a line!

• Finish induction proof of the binomial theorem

• 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!