To solve the expression using the inverse relationship, let’s consider the given information that [tex]\( i = \sqrt{-1} \)[/tex].
1. Understand the definition of [tex]\( i \)[/tex]: The imaginary unit [tex]\( i \)[/tex] is defined as [tex]\( i = \sqrt{-1} \)[/tex]. This is a fundamental concept in complex numbers.
2. Express [tex]\( i^2 \)[/tex]: We need to find the value of [tex]\( i^2 \)[/tex].
3. Square [tex]\( i \)[/tex]:
[tex]\[
i^2 = (\sqrt{-1})^2
\][/tex]
4. Simplify the expression: When you square [tex]\( \sqrt{-1} \)[/tex], the square and the square root cancel each other out, leaving you with:
[tex]\[
i^2 = -1
\][/tex]
Thus, the value of [tex]\( i^2 \)[/tex] is [tex]\(-1\)[/tex]. Therefore, [tex]\( i^2 = \boxed{-1} \)[/tex].
