Understanding De Moivre's Theorem and Riemann Sums

[songoku]

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 :

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

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

 

[chrispb]

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

 

[songoku]

Hi chris

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

Oh my...riemann sum...