- #1

MaxManus

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## Homework Statement

z is a complex number different from 1 and n >= 1 is an integer

[tex] 1 + z + z^2+ ... + z^n = \frac{z^{n+1} - 1}{z-1} [/tex]

show that:

[tex] \sin(\theta) + \sin(2 \theta)+ ... \sin(n \theta) = \frac{ \sin(n \theta/2) \sin((n+1) \theta / 2)}{\sin(\theta / 2)}[/tex]

## The Attempt at a Solution

First I I am both sides and De Moivres formula

[tex] Im( 1 + z + z^2+ ... + z^n) = r \sin( \theta) + r^2 \sin(2 \theta) + ... r^n \sin(n \theta) [/tex]

[tex] Im( \frac{z^{n+1} - 1}{z-1} ) = \frac{r^n \sin((n+1) \theta)}{\sin(\theta)} [/tex]

## Homework Statement

Can anyone give me a hint from here or tell me if I am on the wrong track