객관식
Simplify the power of .
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1. Equations and Inequalities
Powers of i
Multiple Choice
Simplify the power of .
A
B
-1
C
D
1
검증된 단계별 안내1
Recognize that the problem involves simplifying a power of the imaginary unit, i, where i is defined as the square root of -1.
Recall the powers of i cycle every four: i^1 = i, i^2 = -1, i^3 = -i, and i^4 = 1. This cycle repeats for higher powers.
To simplify i^{85}, determine the remainder when 85 is divided by 4, since the powers of i repeat every 4.
Calculate 85 mod 4, which gives the remainder of 1. This means i^{85} is equivalent to i^1.
Conclude that i^{85} simplifies to i, based on the cycle of powers of i.
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