Simplify the power of i.
-$\frac { 1 } { \mathrm { i } ^ { - 20 } }$
A) i
B) 1
C) -i
D) -1

Name: Simplify the power of i. -$\frac { 1 } { \mathrm { i } ^ { - 20 } }$ A) i B) 1 C) -i D) -1
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Question

Quizplus · Accepted Answer

The power of $i$ cycles every 4 powers: $i^1 = i$, $i^2 = -1$, $i^3 = -i$, $i^4 = 1$, and then it repeats. Since $-20$ is divisible by 4, $i^{-20} = 1$. Therefore, $\frac{1}{i^{-20}} = \frac{1}{1} = 1$.

Simplify the Power of I 1i−20\frac { 1 } { \mathrm { i } ^ { - 20 } }i−201​

Simplify the Power of I $\frac { 1 } { \mathrm { i } ^ { - 20 } }$