# Proof complex numbers sum question

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(Original post by

Just copy and paste

**Adacic**)Just copy and paste

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#5

(Original post by

Excuse if my Latex doesn't work

$$\sum_{r=1}^n cos(r\theta)$$ = $$\frac{cos(0.5(n+1)\theta)(sin( 0.5n\theta)}{sin(0.5\theta)}$$

**psycholeo**)Excuse if my Latex doesn't work

$$\sum_{r=1}^n cos(r\theta)$$ = $$\frac{cos(0.5(n+1)\theta)(sin( 0.5n\theta)}{sin(0.5\theta)}$$

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(Original post by

Use [t e x] and [/ t e x] without the spaces around the whole thing and ditch the dollar signs.

**ghostwalker**)Use [t e x] and [/ t e x] without the spaces around the whole thing and ditch the dollar signs.

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#7

(Original post by

Thanks

**psycholeo**)Thanks

Additionally, if you make your first command "\displaystyle" the typset is slightly larger, and the limits on the summation will be above and below the sigma, rather than after it.

Anyhow, to the question itself.

Have you made any progress/working?

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(Original post by

np.

Additionally, if you make your first command "\displaystyle" the typset is slightly larger, and the limits on the summation will be above and below the sigma, rather than after it.

Anyhow, to the question itself.

Have you made any progress/working?

**ghostwalker**)np.

Additionally, if you make your first command "\displaystyle" the typset is slightly larger, and the limits on the summation will be above and below the sigma, rather than after it.

Anyhow, to the question itself.

Have you made any progress/working?

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#10

So if you denote , and also note De Moivre's Theorem, then we have that:

Can you notice what sort of series this is, hence finish it off from there?

__N.B.__denotes which is the real part of the complex number .

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#12

(Original post by

How would I do that? Sorry am really confused

**psycholeo**)How would I do that? Sorry am really confused

Do you understand what I’ve written?

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#13

(Original post by

It's easy to see that you are essentially summing up the real parts of complex numbers numbers with magnitude 1.

So if you denote , and also note De Moivre's Theorem, then we have that:

Can you notice what sort of series this is, hence finish it off from there?

**RDKGames**)It's easy to see that you are essentially summing up the real parts of complex numbers numbers with magnitude 1.

So if you denote , and also note De Moivre's Theorem, then we have that:

Can you notice what sort of series this is, hence finish it off from there?

__N.B.__denotes which is the real part of the complex number .
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#14

(Original post by

Never seen that R notation before

**3pointonefour**)Never seen that R notation before

https://tex.stackexchange.com/questi...maginary-parts

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#15

(Original post by

Never seen that R notation before

**3pointonefour**)Never seen that R notation before

**\mathrm{Re}**everywhere as opposed to just

**\Re**when typesetting.

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#16

(Original post by

Never seen that R notation before

**3pointonefour**)Never seen that R notation before

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#17

(Original post by

If you mean you aren't familiar with taking real/imaginary parts or complex number in general, there's a way to get it without using them, but it's probably easier with them.

**ftfy**)If you mean you aren't familiar with taking real/imaginary parts or complex number in general, there's a way to get it without using them, but it's probably easier with them.

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