Find the power of i.
-$\mathrm { i } ^{15}$
A) -1
B) 1
C) -i
D) i

Name: Find the power of i. -$\mathrm { i } ^{15}$ A) -1 B) 1 C) -i D) i
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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. $i^{15}$ can be simplified as $i^{(4\cdot3+3)} = (i^4)^3 \cdot i^3$. Since $i^4 = 1$, this simplifies to $1^3 \cdot i^3 = i^3 = -i$.

Find the Power of I i15\mathrm { i } ^{15}i15 A) -1 B) 1 C) -I D) I

Find the Power of I $\mathrm { i } ^{15}$ A) -1
B) 1
C) -I
D) I