1. ## complex number equation

I'm trying to get the 4 solutions for this:
$\displaystyle w^4 = -8 +(8*3^\frac{1}{2})i$

In cis form and after applying de Moivre's theorem I get:

$\displaystyle 2cis( \frac{-\pi}{12} +\frac{1}{2}k\pi)$

Where k is varying integer.

I've checked several times and I can't see where I'm wrong.
Help appreciated!

2. ## Re: complex number equation

Originally Posted by elieh
I'm trying to get the 4 solutions for this:
$\displaystyle w^4 = -8 +8*3^\frac{1}{2}$

In cis form and after applying de Moivre's theorem I get:

$\displaystyle 2cis( \frac{-\pi}{12} +\frac{1}{2}k\pi)$

Where k is varying integer.

I've checked several times and I can't see where I'm wrong.
Help appreciated!
Have you written that correctly?
OR should it be $\displaystyle w^4 = -8 +8\sqrt3\color{red}\mathbf{i}$

I edited it

4. ## Re: complex number equation

Originally Posted by elieh
I'm trying to get the 4 solutions for this:
$\displaystyle w^4 = -8 +(8*3^\frac{1}{2})i$
$\displaystyle 2cis( \frac{-\pi}{12} +\frac{1}{2}k\pi)$
You have the argument wrong.
The only thing to add is $\displaystyle k=0,1,2,3$

5. ## Re: complex number equation

But I don't get whole numbers to put in my answer which should be in the form a+bi

6. ## Re: complex number equation

Originally Posted by elieh
But I don't get whole numbers to put in my answer which should be in the form a+bi
$\displaystyle \text{Arg}\left( { - 8 + 8\sqrt 3 i} \right) = \pi + \arctan \left( {\frac{{8\sqrt 3 }}{{ - 8}}} \right) = \frac{{2\pi }}{3}$

Now $\displaystyle \frac{2\pi}{3}\frac{1}{4}=\frac{\pi}{6}$

7. ## Re: complex number equation

That works, Thanks.
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