de Moivre's Theorem

The value of 

 $\left(1+i\sqrt{3}\right)^6$  is

• 64

• -64

• 1

• 2

Tags

CCSS.HSN.CN.B.4

The value of

 $\frac{1}{\left(\cos\theta+i\sin\theta\right)^6}$  is

•  $-\cos6\theta-i\sin6\theta$  

•  $\cos6\theta+i\sin6\theta$  

•  $\cos6\theta-i\sin6\theta$  

•  $-\cos6\theta+i\sin6\theta$  

Tags

CCSS.HSN.CN.B.4

 $\left(\cos\ \frac{\pi}{6}\ -\ i\sin\ \frac{\pi}{6}\right)^{12}\ is\ equal\ to$  

• -i

• -1

• i

• 1

Tags

CCSS.HSN.CN.B.4

 $\cos4\theta$  is eqauivalent to

•  $8\cos^4\theta+8\cos^2\theta+1$  

•  $8\cos^4\theta-8\cos^2\theta+1$  

•  $8\cos^4\theta-8\cos^2\theta-1$  

•  $8\cos^4\theta+8\cos^2\theta-1$  

Tags

CCSS.HSF.TF.C.9

 $\sin4\theta$   is equivalent to

•  $8\cos^3\theta\sin\theta+8\cos\theta\sin^3\theta$  

•  $4\cos^3\theta\sin\theta+4\cos\theta\sin^3\theta$  

•  $4\cos^3\theta\sin\theta-4\cos\theta\sin^3\theta$  

•  $8\cos^3\theta\sin\theta-4\cos\theta\sin^3\theta$  

Tags

CCSS.HSF.TF.C.9

 $If\ z\ =\ \cos\theta\ +i\sin\theta,\ the\ value\ of\ z^3+\frac{1}{z^3}\ is$  

•  $2\cos3\theta$  

•  $\cos3\theta$  

•  $i\sin3\theta$  

•  $2i\sin3\theta$  

Tags

CCSS.HSN.CN.B.4

 $-4\sqrt{3}+4i$  can be expressed in the form  $re^{i\theta}$  as

•  $8e^{\frac{5\pi i}{6}}$  

•  $8e^{-\frac{\pi i}{6}}$  

•  $4e^{\frac{5\pi i}{6}}$  

•  $4e^{-\frac{\pi i}{6}}$  

Tags

CCSS.HSN.CN.B.4

Which of the following is correct?

• $e^{2\theta i}=\sin2\theta+i\cos2\theta$

• $e^{2\theta i}=\cos\theta+2i\sin\theta$

• $e^{2\theta i}=\cos2\theta+i\sin2\theta$

• $e^{2\theta i}=2\left(\cos\theta+i\sin\theta\right)$

Tags

CCSS.HSN.CN.B.4

 $e^{-i\pi}$  is equal to

• -i

• i

• 1

• -1

Tags

CCSS.HSN.CN.B.4

 $e^{1+i\theta}$  is equal to

•  $e^{\cos\theta+i\sin\theta}$  

•  $e\left(\cos\theta+i\sin\theta\right)$  

•  $\cos\left(1+i\right)+j\sin\left(1+i\right)$  

•  $ei\sin\theta$  

Tags

CCSS.HSN.CN.B.4