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Complex Number Questions

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frog0101:
Hi, I have been unable to do these questions (any help would be great):
1. Simplify sin(x)+sin(2x)+...+sin(nx)

2. Let z^13=w and w^11=z. Prove that Im(z)=sin{(m*pi)/n} if both z and w are complex numbers, where m and n are positive integers with no common factors.

Thanks

RuiAce:

RuiAce:



The fact that \(m\) and \(n\) have no common factors just means that it is a fraction simplified to its lowest terms. For example, if we had something like \( \frac{2}{142}\), we could just simplify it down to \( \frac{1}{71}\) instead.

frog0101:
Thanks so much RuiAce!!

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