PSAT Math Multiple-Choice Question 694: Answer and Explanation
Question: 694
If
- A. -162
- B. -6
- C. 162i
- D. 162
Correct Answer: A
Explanation:
(A) Remember the cycle of how in repeats as we increase the integer n> by 1 each time:
i2 = -1
i3 = -i
i4 = 1
Therefore, 2i2 = 2(-1) = -2.
For (3i)4, we have to remember to raise both the 3 and the i to the fourth power:
34 = 81
i4 = 1
(3i)4 = (81)(1) = 81
Multiply the two terms together:
2i2(3i)4 = (-2)(81) = -162
The answer is choice (A).
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