Simplify the expression. $$i ^ { 43 }$$
A) $- i$
B) $- 1$
C)1
D) $i$
E)0

Name: Simplify the expression. \[i ^ { 43 }\] A) $- i$ B) $- 1$ C)1 D) $i$ E)0
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Question

Quizplus · Accepted Answer

The powers of $i$ cycle in a pattern: $i^1 = i$, $i^2 = -1$, $i^3 = -i$, $i^4 = 1$, and then the pattern repeats. For $i^{43}$, divide 43 by 4 to find the remainder. Since $43 = 4 \times 10 + 3$, the remainder is 3, so $i^{43} = i^3 = -i$.

Simplify the Expression i43i ^ { 43 }i43 A) −i- i−i B) −1- 1−1

Simplify the Expression $i ^ { 43 }$ A) $- i$ B) $- 1$