SAT Math Multiple Choice Question 628: Answer and Explanation

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Test Information

Question: 628

13. If Images, which of the following is NOT equal to i3 + i?

  • A. (2i)2 + 4
  • B. 2 - 2i4
  • C. 2i2 - 2
  • D. i4 - 1

Correct Answer: C

Explanation:

C

Additional Topics (complex numbers) HARD

To solve this without a calculator, you must be able to evaluate a few low powers of i. Recall from Chapter 10, Lesson 10, that i0 = 1, i1 = i, i2 = -1, i3 = -i, and i4 = 1. Therefore i3 + i = -i + i = 0. Now, it's just a matter of finding the choice that does NOT equal 0.

(A) (2i)2 + 4 = -4 + 4 = 0

(B) 2 - 2i4 = 2 - 2 = 0

(C) 2i2 - 2 = -2 - 2 = -4

(D) i4 - 1 = 1 - 1 = 0

Therefore, the correct answer is (C).

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