SAT Math Multiple Choice Question 642: Answer and Explanation

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Question: 642

12. If i2k = 1, and Images, which of the following must be true about k?

  • 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. Images is an integer.

Correct Answer: D

Explanation:

D

Special Topics (complex numbers) MEDIUM-HARD

Recall from Chapter 10, Lesson 10, that in = 1 if and only if n is a multiple of 4. (If you need refreshing, just confirm that 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. If k is a multiple of 2, then k/2 must be an integer. Choice (A) is incorrect, because k = 2 is a solution, but 2 is not a multiple of 4. Choice (B) is incorrect because k = -2 is a solution, and -2 is not a positive integer. Choice (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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