Simplify the power of i.
-$\mathrm { i } ^ { - 11 }$
A) $- \mathrm { i }$
B) $i$
C) $- 1$
D) 1

Name: Simplify the power of i. -$\mathrm { i } ^ { - 11 }$ A) $- \mathrm { i }$ B) $i$ C) $- 1$ D) 1
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Question

Quizplus · Accepted Answer

The powers of i cycle every four: $i^1 = i$, $i^2 = -1$, $i^3 = -i$, $i^4 = 1$. For negative powers, $i^{-n} = 1/i^n$. Since $i^4 = 1$, $i^{-11} = i^{-(11 \mod 4)} = i^{-3} = 1/i^3 = -i$.

Simplify the Power of I i−11\mathrm { i } ^ { - 11 }i−11

Simplify the Power of I $\mathrm { i } ^ { - 11 }$