# DeMoivre's Theorem

• Nov 11th 2012, 09:29 AM
derek1008
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
• Nov 11th 2012, 09:37 AM
skeeter
Re: DeMoivre's Theorem
computation of what?
• Nov 11th 2012, 09:51 AM
derek1008
Re: DeMoivre's Theorem
computation involving z using DeMoivre's Theorem
• Nov 11th 2012, 10:03 AM
a tutor
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?
• Nov 11th 2012, 10:55 AM
Plato
Re: DeMoivre's Theorem
Quote:

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?
• Nov 11th 2012, 11:00 AM
derek1008
Re: DeMoivre's Theorem
The question asks to identify a computation involving z that can be performed using DeMoivre's Theorem.
• Nov 11th 2012, 11:44 AM
Plato
Re: DeMoivre's Theorem
Quote:

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
$\displaystyle z^{\alpha}=\exp\left(\frac{i\pi\alpha}{3}\right)$.
• Nov 11th 2012, 11:48 AM
skeeter
Re: DeMoivre's Theorem
Quote:

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 $\displaystyle \theta = \frac{\pi}{3}$