Re: complex number equation

Quote:

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} $

Re: complex number equation

Sorry! my bad,

I edited it

Re: complex number equation

Quote:

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 $\displaystyle k=0,1,2,3$

Re: complex number equation

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

Re: complex number equation

Quote:

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

Re: complex number equation