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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 578 (page 856)

In the following exercises, simplify.
$i^{255}$

Short Answer

Expert verified

The simplified form is $- i$ .

Step by step solution

01

Step 1. Given information.

The given imaginary number is $i^{255}$ .

02

Step 2. Simplify the power.

We know that,

$i = \sqrt{- 1} i^{2} = - 1 i^{3} = - i i^{4} = 1$

Divide the power by $4$ and rewrite,

localid="1646857845922" $i^{255} = i^{4 \cdot 63 + 3} = {(i^{4})}^{63} \cdot i^{3} = {(1)}^{63} \cdot i^{3} = 1 \cdot i^{3} = - i$

Therefore, the simplified form islocalid="1646857833477" $- i$

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Most popular questions from this chapter

In the following exercises, simplify using absolute value signs as needed.

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What is the difference between $9^{2}$ and $\sqrt{9}$ ?

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