AnswersPrecalculusPowers and Roots of Complex Numbers

Powers and Roots of Complex Numbers Answers

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1
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The modulus of z4 would be .

A
3
B
9
C
27
D
81
2
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The coefficient in front of the argument (or angle) of z4 would be .

A
2
B
3
C
4
D
9
3

Step A:

A
distributive property
B
trigonometric sum identity
C
product of powers
D
substitution property
4

Step D:

A
distributive property
B
trigonometric sum identity
C
product of powers
D
substitution property
5

What is (1 − i)6?

A
–8
B
8i
C
8
D
–8i
6

The roots are located on a circle with center at the pole and radius of .

A
2
B
4
C
8
D
16
7

The arguments of two successive roots differ by π units along the circumference of a circle.

A
1/2
B
1
C
2
8

What is the distance along the unit circle between any two successive 8th roots of 1?

A
Option
B
Option
C
Option
D
Option
9

Step C:

A
distributive property
B
trigonometric sum identity
C
product of powers
D
substitution property

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