# simple complex numbers proof

• Sep 3rd 2009, 02:22 PM
Mr.Ree
simple complex numbers proof
If z = cisΘ, show that cos(nΘ) = 1/2 (z^n + (1/z^n))

I have done:

z^n = (cisΘ)^n = cos(nΘ) + isin(nΘ)

cos(nΘ) = z^n - isin(nΘ)

Don't know where to go from here. Any help or advice would be greatly appreciated.
• Sep 3rd 2009, 02:27 PM
Matt Westwood
Now do $z^{-n}$ and add it to what you've already got.
• Sep 3rd 2009, 02:47 PM
Mr.Ree
I've got it now =]
Thank you very much