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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 solve for [tex]\( i^3 \)[/tex] where [tex]\( i = \sqrt{-1} \)[/tex]:

1. Start by knowing the fundamental property of [tex]\( i \)[/tex], which is:
[tex]\[ i = \sqrt{-1} \][/tex]

2. Next, calculate [tex]\( i^2 \)[/tex]:
[tex]\[ i^2 = (\sqrt{-1})^2 = -1 \][/tex]

3. Now, use the value of [tex]\( i^2 \)[/tex] to find [tex]\( i^3 \)[/tex]:
[tex]\[ i^3 = i \cdot i^2 \][/tex]

4. Substitute [tex]\( i^2 \)[/tex] with [tex]\(-1\)[/tex]:
[tex]\[ i^3 = i \cdot (-1) = -i \][/tex]

So, the value of [tex]\( i^3 \)[/tex] is:
[tex]\[ -i \][/tex]

Therefore, [tex]\( i^3 \)[/tex] evaluates to [tex]\(-i\)[/tex]. Among the given choices, the correct answer is:
[tex]\[ \boxed{-i} \][/tex]
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