Simplify the power of i.
-$i ^ { 61 }$
A) 1
B) $- \mathrm { i }$
C) $\mathrm { i }$
D) $- 1$

Name: Simplify the power of i. -$i ^ { 61 }$ A) 1 B) $- \mathrm { i }$ C) $\mathrm { i }$ D) $- 1$
Brand: Quizplus
Rating: 4.8 (41 reviews)

Question

Quizplus · Accepted Answer

The powers of $i$ cycle through a pattern: $i^1 = i$, $i^2 = -1$, $i^3 = -i$, $i^4 = 1$, and then the pattern repeats. $i^{61}$ can be simplified by dividing 61 by 4, which gives a remainder of 1. Therefore, $i^{61} = i^{4 \cdot 15 + 1} = (i^4)^{15} \cdot i^1 = 1^{15} \cdot i = i$.

Simplify the Power of I i61i ^ { 61 }i61 A) 1 B)

Simplify the Power of I $i ^ { 61 }$ A) 1
B)