1. ## DeMoivre's Theorem

Let z= 1/2+ square root of 3 over 2i
Perform the computation using DeMoivre's theorem and explain why this theorem makes the computation easier

2. ## Re: DeMoivre's Theorem

computation of what?

3. ## Re: DeMoivre's Theorem

computation involving z using DeMoivre's Theorem

4. ## Re: DeMoivre's Theorem

It's not even clear what z is. Do you mean $\displaystyle \frac{1}{2}+\frac{\sqrt{3}}{2}i$?

If so what do you want to do with it?

5. ## Re: DeMoivre's Theorem

Originally Posted by derek1008
Let z= 1/2+ square root of 3 over 2i
Perform the computation using DeMoivre's theorem and explain why this theorem makes the computation easier
$\displaystyle \frac{1}{2}+\frac{\sqrt{3}}{2}i=\exp\left(\frac{i\ pi}{3}\right)$.

Now what do you want done?

6. ## Re: DeMoivre's Theorem

The question asks to identify a computation involving z that can be performed using DeMoivre's Theorem.

7. ## Re: DeMoivre's Theorem

Originally Posted by derek1008
The question asks to identify a computation involving z that can be performed using DeMoivre's Theorem.

If $\displaystyle \alpha\in\mathbb{R}$, a real number, then if
$\displaystyle z=\frac{1}{2}+\frac{\sqrt{3}}{2}i=\exp\left(\frac{ i\pi}{3}\right)$ we have
$\displaystyle z^{\alpha}=\exp\left(\frac{i\pi\alpha}{3}\right)$.

8. ## Re: DeMoivre's Theorem

Originally Posted by derek1008
The question asks to identify a computation involving z that can be performed using DeMoivre's Theorem.
ok ...

$\displaystyle z = r(\cos{\theta} + i \sin{\theta})$

if $\displaystyle z = \frac{1}{2} + \frac{\sqrt{3}}{2} i$ , then $\displaystyle r = 1$ and $\displaystyle \theta = \frac{\pi}{3}$