1. ## Complex Numbers

Hi guys, hopefully this is in the correct thread.

I have two questions that are bugging me...:

1) Express the following complex number in the exponential polar form: (2-2 x sqrt(3) x i)^13

2) Using the complex exponential, express cos(4theda) in terms of cos(theda).

Any help would be greatly appreciated!

Thanks -

2. ## Re: Complex Numbers

Originally Posted by Jonathancrowden774
1) Express the following complex number in the exponential polar form: (2-2 x sqrt(3) x i)^13

2) Using the complex exponential, express cos(4theda) in terms of cos(theda).
$|2-2\sqrt3i|=4$ and $\text{Arg}(2-2\sqrt3i)=\frac{-\pi}{3}$

$\cos(t)=\frac{e^{it}+e^{-it}}{2}$

3. ## Re: Complex Numbers

Originally Posted by Plato
$|2-2\sqrt3i|=4$ and $\text{Arg}(2-2\sqrt3i)=\frac{-\pi}{3}$

$\cos(t)=\frac{e^{it}+e^{-it}}{2}$
I would like to add for the second part,
$e^{4i\theta}={(e^{i\theta})}^4}\Rightarrow cos(4\theta)+isin(4\theta)={(cos\theta+isin\theta) }^4$

Expand the right hand side using Binomial Expansion and then equate the real parts to get the value of $cos4\theta$.