DeMoivre's Theorem of Nth Roots

 $r^{\left(\frac{1}{n}\right)}\left[\cos\left(\frac{\theta+360k}{n}\right)+i\sin\left(\frac{\theta+360k}{n}\right)\right]$  

What is this formula called?

• Rational Roots Theorem

• Euler's Formula

• DeMoivre's Theorem of Nth Roots

• Intermediate Value Theorem

Tags

CCSS.HSN.CN.B.4

In order to find the 4th roots of  $625\left(\cos448\ +\ i\sin448\right)$  

What is  $r^{\left(\frac{1}{n}\right)}$  ?

(a)  

In order to find the 4th roots of  $625\left(\cos448\ +\ i\sin448\right)$  

What is  $\frac{\theta}{n}$  ?
  
This is the angle you use for the first root!

(a)  

In order to find the 4th roots of  $625\left(\cos448\ +\ i\sin448\right)$  

What is  $\frac{360}{n}$  ? 

This is how much you add each time!

(a)  

Find the 4th roots of  $625\left(\cos448\ +\ i\sin448\right)$  

Check ALL that apply

• 5(cos112 + isin112)

• 5(cos202 + isin202)

• 5(cos224 + isin224)

• 5(cos292+isin292)

• 5(cos382+isin382)

Which formula should be used if we are given theta in radians?

•  $r^{\left(\frac{1}{n}\right)}\left[\cos\left(\frac{\theta+360k}{n}\right)+i\sin\left(\frac{\theta+360k}{n}\right)\right]$  

•  $r^{\left(\frac{1}{n}\right)}\left[\cos\left(\frac{\theta+2\pi k}{n}\right)+i\sin\left(\frac{\theta+2\pi k}{n}\right)\right]$  

Tags

CCSS.HSN.CN.B.4

If you are asked to find the cubed roots of  $64\left(\cos435\degree+i\sin435\degree\right)$ , how many answers should you have?

• 1

• 2

• 3

• 4

Which of the following is the correct cubed roots of  $64\left(\cos435\degree+i\sin435\degree\right)$ 

•  $4\left(\cos145\degree+i\sin145\degree\right)$  

   $4\left(\cos290\degree+i\sin290\degree\right)$ 
   $4\left(\cos435\degree+i\sin435\degree\right)$   
  

•  $4\left(\cos145\degree+i\sin145\degree\right)$  

   $4\left(\cos263\degree+i\sin263\degree\right)$ 
   $4\left(\cos383\degree+i\sin383\degree\right)$