Day 3 in Mat430

Today:

• Announcements
  • There's a talk at 3:00, that some of you might like to attend, featuring department chair Steve Wilkinson (3:00 in ST 111). Here's his blurb.

• Sections 3 and 4 today: 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!

• Section 5: polar form
  • If we get a chance, we'll introduce the notion of representing complex numbers using a polar representation
    • Arg versus arg (principal value)
    • the non-uniqueness of zero....