Imaginary Numbers

The imaginary number  $i$  is defined as

• -1

•  $\sqrt{-1}$  

•  $\sqrt{-4}$  

•  $\left(-1\right)^2$  

Tags

CCSS.HSN.CN.A.1

Which of the following is equivalent to  $\sqrt{-128}$ ?

•  $8\sqrt{2}$  

•  $8i$  

•  $-8\sqrt{2}$  

•  $8i\sqrt{2}$  

The sum  $\sqrt{-9}+\sqrt{-16}$ is equal to

•  $5$  

•  $5i$  

•  $7i$  

•  $7$  

Tags

CCSS.HSN.CN.A.2

Which of the following powers of  $i$  is not equal to one?

•  $i^{16}$  

•  $i^{26}$  

•  $i^{32}$  

•  $i^{48}$  

Tags

CCSS.HSN.CN.A.2

Which of the following represents all solutions to the equation  $\frac{1}{3}x^2+10=7$ ?

•  $x=\pm3i$  

•  $x=\pm5i$  

•  $x=\pm i$  

•  $x=\pm2i$  

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Which of the following represents the solution set of  $\frac{1}{2}x^2-12=-37$ ?

•  $\pm7i$  

•  $\pm7i\sqrt{2}$  

•  $\pm5i\sqrt{2}$  

•  $\pm3i\sqrt{2}$  

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

Simplify each of the following into either  $-1,\ 1,\ i\ ,\ -i$  

 $i^2$  

•   $i$  

•  $-1$ 

•  $-i$  

•  $1$  

Tags

CCSS.HSN.CN.A.1

Simplify each of the following into either  $-1,\ 1,\ i\ ,\ -i$  

 $i^3$  

•   $i$  

•  $-1$ 

•  $-i$  

•  $1$  

Tags

CCSS.HSN.CN.A.1

Simplify each of the following into either  $-1,\ 1,\ i\ ,\ -i$  

 $i^{11}$  

•   $i$  

•  $-1$ 

•  $-i$  

•  $1$  

Tags

CCSS.HSN.CN.A.2

Simplify each of the following into either  $-1,\ 1,\ i\ ,\ -i$  

 $i^{41}$  

•   $i$  

•  $-1$ 

•  $-i$  

•  $1$  

Tags

CCSS.HSN.CN.A.2