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Homework Help: Ask about exam's syllabus

  1. Jan 27, 2010 #1
    I read my exam's syllabus and come across these topic :

    1. De Moivre’s theorem for an integral exponent (without proof)

    2. The idea of area under a curve as the limit of a sum of areas of rectangles.

    My teacher never taught the class about this topic. I want to ask what these topics about.

    De Moivre’s theorem for an integral exponent

    Is this the meaning :

    [tex]\int ~e^{i \theta}~d\theta~=~\int ~(\cos~\theta~+~i\sin\theta)~d\theta[/tex]

    Then we consider i as a constant and just do simple integral?

    For the second one, I don't know the meaning...

    Can anyone give me a clue what I shoud study about these two topics. Thanks
  2. jcsd
  3. Jan 27, 2010 #2
    1) De Moivre's theorem states that e^inx = (cos x + i sin x)^n = cos nx + i sin nx. Once you believe e^ix = cos x + i sin x, this is very easy to demonstrate. He's specifically referring to n being an integer, but it should be true for n being any real number, as far as I know.

    2) This is the notion of a Riemann sum, which defines the Riemann integral. See here: http://en.wikipedia.org/wiki/Riemann_sum
  4. Jan 27, 2010 #3
    Hi chris

    About the integral part of De Moivre's theorem, Is what I posted right?

    Oh my...riemann sum...
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