Simplify the power of i.
-$\mathrm { i } ^ { - 47 }$
A) 1
B) -i
C) -1
D) i

Name: Simplify the power of i. -$\mathrm { i } ^ { - 47 }$ A) 1 B) -i C) -1 D) i
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Question

Quizplus · Accepted Answer

The powers of $i$ cycle through four different values: $i^1 = i$, $i^2 = -1$, $i^3 = -i$, and $i^4 = 1$. For any negative exponent, you can find the equivalent positive exponent that gives the same result. Since $-47$ is equivalent to $4n + 1$ for some integer $n$ (specifically, $n = -12$ here), $i^{-47} = i^{4(-12) + 1} = i^{1} = i$.

Simplify the Power of I i−47\mathrm { i } ^ { - 47 }i−47

Simplify the Power of I $\mathrm { i } ^ { - 47 }$