Powers and Roots of Complex Numbers

Question 1

What is 5 Left-bracket cosine (StartFraction pi Over 4 EndFraction) + I sine (StartFraction pi Over 4 EndFraction) right-bracket raised to the 3rd power?

Revolt · Accepted Answer

Answer image: //media.edgenuity.com/EVresources/0fe2bfba4d5875606cebadfd5d2cdad2.png

Question 2

Consider the number . What happens when z is raised to successively increasing powers?

Revolt · Accepted Answer

✔ 10; The modulus increases by a factor of .: 10; The argument increases by π over 3.: 5

Question 3

12✔ 510

Revolt · Accepted Answer

✔ 5

Question 4

Consider the complex number z = 27i. What are the characteristics of the cube roots of z?

Revolt · Accepted Answer

✔ 3; The cube roots are located on a circle with center at the pole and radius of .: 3; The cube roots have arguments which differ by π over 3.: 2

Question 5

1✔ 23

Revolt · Accepted Answer

✔ 2

Question 6

What is the correct justification for the indicated steps?

Revolt · Accepted Answer

Step C:: distributive property; Step D:: trigonometric sum identity; Step E:: factoring

Question 7

✔ trigonometric sum identitydistributive propertyfactoringproduct of powers

Revolt · Accepted Answer

✔ trigonometric sum identity

Question 8

product of powersdistributive property✔ factoringtrigonometric sum identity

Revolt · Accepted Answer

✔ factoring

Question 9

What is (one-half, I StartFraction StartRoot 3 EndRoot Over 2 EndFraction) Superscript 5 ?

Revolt · Accepted Answer

Answer image: //media.edgenuity.com/EVresources/3b42e42c9f1dbb57d753e97b57d0cc42.png

Question 10

Consider the graph of z. Which lettered point represents z2?

Revolt · Accepted Answer

C

Powers and Roots of Complex Numbers Answers

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