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If [tex]\(i = \sqrt{-1}\)[/tex], what is the value of [tex]\(i^3\)[/tex]?

A. [tex]\(-1\)[/tex]
B. [tex]\(i\)[/tex]
C. [tex]\(1\)[/tex]
D. [tex]\(-i\)[/tex]

Sagot :

GinnyAnswer
To determine the value of [tex]\(i^3\)[/tex], we must understand the properties of the imaginary unit [tex]\(i\)[/tex], where [tex]\(i = \sqrt{-1}\)[/tex].

First, let's list a few basic powers of [tex]\(i\)[/tex]:

- [tex]\(i^1 = i\)[/tex]
- [tex]\(i^2 = i \cdot i = -1\)[/tex]
- [tex]\(i^3 = i^2 \cdot i = -1 \cdot i = -i\)[/tex]

So we see that:

[tex]\[ i^3 = -i \][/tex]

Therefore, the value of [tex]\(i^3\)[/tex] is [tex]\( \boxed{-i} \)[/tex].
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