Powers and Roots of Complex Numbers

Question 1

Which of the following are square roots of ? Check all that apply.

Revolt · Accepted Answer

Answer image: https://r07.core.learn.edgenuity.com//media.edgenuity.com/EVresources/d1dbcd395d60fb5a385f88bee8760532.png; Answer image: https://r07.core.learn.edgenuity.com//media.edgenuity.com/EVresources/9af8d8d7cf3b67f2601d301f79a42d95.png

Question 2

Question 2

Revolt · Accepted Answer

2

Question 3

Question 3

Revolt · Accepted Answer

factoring

Question 4

Determine which regions contain cube roots of −1. Check all that apply.

Revolt · Accepted Answer

on real axis; quadrant 1; quadrant 4

Question 5

Consider the complex number z = 27i. What are the characteristics of the cube roots of z? Use the drop-down menus to complete each sentence. The cube roots are located on a circle with center at the pole and radius of . The cube roots have arguments which differ by π over 3.

Revolt · Accepted Answer

3; Selection 1: 3; Selection 2: 2

Question 6

Determine which regions contain cube roots of 8i. Check all that apply.

Revolt · Accepted Answer

on imaginary axis; quadrant 1; quadrant 2

Question 7

What is the correct justification for the indicated steps? Step C: Step D: Step E:

Revolt · Accepted Answer

distributive property; Selection 1: distributive property; Selection 2: trigonometric sum identity; Selection 3: factoring

Question 8

What is raised to the 3rd power?

Revolt · Accepted Answer

Answer image: https://r07.core.learn.edgenuity.com//media.edgenuity.com/EVresources/0fe2bfba4d5875606cebadfd5d2cdad2.png

Question 9

What is ?

Revolt · Accepted Answer

One-half minus I StartFraction StartRoot 3 EndRoot Over 2 EndFraction

Question 10

Consider the graph of z3. Which lettered point represents z?

Revolt · Accepted Answer

B

Powers and Roots of Complex Numbers Answers

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