If i2k= 1, and i2= -1. Which of the following must be true about k ?
Correct answer: A. k is a multiple of 2.
- A. k is a multiple of 2.
- B. k is a positive integer.
- C. When 2k is divided by 4, the remainder is 1.
- D. k/4 is an even integer.
Explanation
in = 1 if and only if n is a multiple of 4. (i4 = 1, i8= 1, i12 = 1, etc.) Therefore, if i2k = 1, then 2k must be a multiple of 4, and therefore, k must be a multiple of 2. When the power is even the answer is 1 or else it is -1. Option B: K is not a positive integer as the answer would then be negative Option C: k is a multiple of 2 and multiplying k with 2, the answer produced would be an even number which would not be completely divisible by 4 and would not give 1 as the remainder, for e.g 2(4)/4=2 Option D: k is supposed to be a multiple of 2 e.g 10/4 = 2.5 , the answer is not going to be an even integer.
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