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]
