If i^2k=1, and i=√-1, which of the following must
be true about k

Answers

Answer 1

If i^2k=1, and i=√-1, the answer choice that must be true about k is D. k/2 is an integer.

Calculations and Parameters

We can recall that i^n= 1 if and only if n is a multiple of 4. (If you need refreshing, just confirm that i^4 = 1, i^8 = 1, i^12 = 1, etc.)

Therefore, if i^2k = 1, then 2k must be a multiple of 4, and therefore, k must be a multiple of 2.

If k is a multiple of 2, then k/2 must be an integer.

Option (A) is incorrect because k = 2 is a solution, but 2 is not a multiple of 4.

Option (B) is incorrect because k = -2 is a solution, and -2 is not a positive integer.

Option (C) is incorrect because k = 2 is a solution, but when 2(2) = 4 is divided by 4, the remainder is 0, not 1.

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The answer choices are:

A. k is a multiple of 4.

B. k is a positive integer.

C. When 2k is divided by 4, the remainder is 1.

D. k/2 is an integer.


Related Questions

Dana’s grandparents gave her a piggy bank with $10 for her birthday. Dana added $2 each week to the piggy bank and recorded how much money she had in it at the end of each week. If she did this for 9 weeks after her birthday, what is the median of the amounts she recorded during these weeks?

Answers

Answer:

MEDIAN= 19

Explanation:

The amounts are 10,12,14,16,18,20,22,24,26,28

18 + 20 = 38

38 / 2 = 19

19 is your median.

Hope I helped <3

Expand.
If necessary, combine like terms.
(x + 5)(x - 5) =

Answers

Answer:

x^2-25

Explanation:

use the foil method - personally works best for me

hope this helps :)

The repeated descriptions of the rituals of shooting the bow (bowing to the other archer, bowing toward the target) are most likely intended to emphasize:


O. the boy's exasperation with the repetitiveness of the archery competition.
O. Tetsuya's and the stranger's connection with their heritage

O.the sacredness of the ritual and the respect with which the archers treat the art.
O. the irony of Tetsuya's and the stranger's feigned respect in the heat of competition.

Answers

The repeated descriptions of the rituals of shooting the bow are most likely intended to emphasize the boy's exasperation with the repetitiveness of the archery competition. The correct option is A.

What is archery?

Archery is the recreational activity, training, or expertise of shooting arrows with a bow. The word is originated from the Latin arcus, which implies "bow."

Archery has historically been employed for hunting and confront. It is primarily a competitive sport and recreational activity in modern times.

The repeated descriptions of archery rituals are most likely intended to highlight the boy's frustration with the archery competition's repetitiveness.

Thus, the correct option is A.

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What is one way John Chapman cared for the earth

Answers

Answer:

by caring for the earth?

Explanation:

by caring for the earth?

Planted a lot of trees and John Chapman established nurseries of apple trees

Models can represent things that are too far away or to small to see true or false?

Answers

Answer:

true

Explanation:

models can represent really anything

soaring toward the light.
Should the writer make this revision?

Answers

Answer:

the light weakens the eye for the future

Explanation:

it is when the writer has been blinded by the light towards him meaning that he cannot see his future or his decisions

tell me a person for narito

Answers

Naruto?

im guessing well i have two one is an emo boy with great sword powerers that is Itachi he kissed this golden hair blue eyes bot named Naruto

(I ship it )

Need help with Information TechnologySBA

Answers

Explanation:

technology SBA(small business administration) information resources management IRM

strategic plan reflects the agency's dedication to optimizing and maintaining the SBA'S IT infastructure indetifying areas for IT effiency and innovation and investing in the IT workforce

What is JAG? In high school

Answers

Answer:

Explanation:

JAG stands for Jobs for American Graduates. It's supposed to help graduates transition into a workplace and get high quality jobs.

The original JAG Model was launched in 1979 in the State of Delaware as a “school-to-work transition program” designed to keep students in school through graduation and help them transition into the work place in quality jobs.

Inhumane factory farming methods have a huge tendency to contribute to environmental
degradation. Explain the connection and motivate why a study on such factors is important.

Answers

Inhumane factory farming methods have a huge tendency to contribute to environmental degradation because  a lot of Factory farms do bring out a lot of noxious air pollutants for example ammonia, hydrogen sulfide, as well as  methane. These emissions are known to have a negatively effect on the human health, animal health, as well as the environment.

What is the link between inhumane factory farming methods and environmental degradation?

The use of the  Inhumane factory farming method is known to be one that has a lot of connection with the harm that is done to the environment. Activities  are known to be done by humans has brought a lot of harm such as environmental degradation through the Cutting down of trees.

Therefore, Inhumane factory farming methods have a huge tendency to contribute to environmental degradation because  a lot of Factory farms do bring out a lot of noxious air pollutants for example ammonia, hydrogen sulfide, as well as  methane. These emissions are known to have a negatively effect on the human health, animal health, as well as the environment.

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