1. ## Alge' Complex

Hi just received some interesting questions based on complex most seems fine but 2 is bit fague to start of....

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Express cos 8 "beta" in terms of cos "beta"
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And
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Show every group of order 3 is isomorphic to C3, the cyclic group of order 3.
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Point me in the right direction and it should be no problem for me.

Thanks

2. Originally Posted by NeloAngelo
Express cos 8 "beta" in terms of cos "beta"
$\displaystyle \cos 8x = \Re ( (\cos x + i\sin x)^8 )$.

Show every group of order 3 is isomorphic to C3, the cyclic group of order 3.
If $\displaystyle |G| = p$ then $\displaystyle G$ is cyclic for prime $\displaystyle p$. That is easy. Let $\displaystyle a\in G$ so that $\displaystyle a\not = e$. Then the order of $\displaystyle a$ must divide $\displaystyle p$ by Lagrange's theorem. Since $\displaystyle p$ is prime it means $\displaystyle a$ has order $\displaystyle p$ and so $\displaystyle G = \left< a \right>$.

3. Wow thx a lot Hax0r