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Which one is not a root of the fourth root of unity.
- a)i
- b)1
- c)i/√2
- d)-i
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Which one is not a root of the fourth root of unity.a)ib)1c)i/√2...
A complex number z such that z 4=1. There are 4 fourth roots of unity and they are 1, i,−1 and−i.
Most Upvoted Answer
Which one is not a root of the fourth root of unity.a)ib)1c)i/√2...
For any integer n, the nth root of a number k is a number that, when multiplied by itself n times, yields k.
Check the options.
Option a, b, d when multipled by itself for 4 times yields 1.
So the answer is c
Check the options.
Option a, b, d when multipled by itself for 4 times yields 1.
So the answer is c
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Which one is not a root of the fourth root of unity.a)ib)1c)i/√2...
One of the roots of unity is a complex number that, when raised to the power of n (where n is the number of roots), results in 1. In the case of the fourth root of unity, there are four roots that satisfy this condition.
Explanation:
Fourth Root of Unity:
- The fourth roots of unity are given by the complex numbers 1, i, -1, and -i.
- These roots can be represented in the complex plane as points evenly spaced around the unit circle.
Identifying the Non-Root:
- The given options are i, 1, i/√2, and -i.
- To determine the non-root, we need to check which of these values do not satisfy the condition of being a fourth root of unity.
Analysis:
- i^4 = 1, so i is a valid fourth root of unity.
- 1^4 = 1, so 1 is also a valid fourth root of unity.
- (-i)^4 = 1, so -i is a valid fourth root of unity.
- (i/√2)^4 = i^4 / √2^4 = 1/2, which is not equal to 1.
Conclusion:
- Therefore, i/√2 is not a root of the fourth root of unity.
- The correct answer is option C: i/√2.
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