Simplify the complex number and write it in standard form.
$- 42 i ^ { 5 }$
A) $- 42 i ^ { 3 }$
B) $42 i ^ { 3 }$
C) $- 42 i$
D) $- 42$
E) $42 i$

Name: Simplify the complex number and write it in standard form. $- 42 i ^ { 5 }$ A) $- 42 i ^ { 3 }$ B) $42 i ^ { 3 }$ C) $- 42 i$ D) $- 42$ E) $42 i$
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Question

Simplify the complex number and write it in standard form. 
 $- 42 i ^ { 5 }$  
A)  $- 42 i ^ { 3 }$
B)  $42 i ^ { 3 }$
C)  $- 42 i$
D)  $- 42$
E)  $42 i$

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. $i^5 = i^{4+1} = i^4 \cdot i^1 = 1 \cdot i = i$. Therefore, $-42i^5 = -42i$.

Simplify the Complex Number and Write It in Standard Form −42i5- 42 i ^ { 5 }−42i5

Simplify the Complex Number and Write It in Standard Form $- 42 i ^ { 5 }$