Simplify the power of i.
-$\frac { 1 } { \mathrm { i } ^ { 41 } }$
A) $- \mathrm { i }$
B) $- 1$
C) 1
D) $\mathrm { i }$

Name: Simplify the power of i. -$\frac { 1 } { \mathrm { i } ^ { 41 } }$ A) $- \mathrm { i }$ B) $- 1$ C) 1 D) $\mathrm { i }$
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Question

Quizplus · Accepted Answer

The powers of i cycle every four: $i^1 = i$, $i^2 = -1$, $i^3 = -i$, $i^4 = 1$. Thus, $i^{41} = i^{(40+1)} = i^1 = i$. Therefore, $\frac{1}{i^{41}} = \frac{1}{i} = -i$.

Simplify the Power of I 1i41\frac { 1 } { \mathrm { i } ^ { 41 } }i411​

Simplify the Power of I $\frac { 1 } { \mathrm { i } ^ { 41 } }$