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].
