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22.07.2019 •
Mathematics
Which of the following expressions is a fourth root of unity? a.) -1 b.) i c.) -i d.) all of the above
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Ответ:
We have to evaluate the fourth roots of unity.
For each natural number say 'n', there are exactly 'n' nth roots of unity which is expressed in the form as
where k=0,1,2,.... n-1
Since we have to evaluate the fourth root of unity.
Therefore, we take k=0,1,2,3 and n=4
So, we get
Now, For k=0, we get our first root as:
First root = 1
Now, for k=1, we get
(Eulers Formula)
So,
So, second root = i
Now, for k=2, we get
(Eulers Formula)
So,
Third root = -1
Now, for k=3, we get
(Eulers Formula)
So,
So, fourth root = -i
Hence, all the fourth roots of unity are 1, i, -1 and -i
Therefore, option D is correct as all the given roots in option A, B and C are the fourth roots of unity.
Ответ:
I am on the same question with u with my hw
Step-by-step explanation:
I need to answer for points