Sure! Let's break this down step-by-step.
1. Understanding [tex]\(i\)[/tex]:
[tex]\[
i = \sqrt{-1}
\][/tex]
Here, [tex]\(i\)[/tex] is defined as the imaginary unit, which is the square root of [tex]\(-1\)[/tex].
2. Square both sides of the equation:
To determine what [tex]\(i^2\)[/tex] is, we square both sides of the equation [tex]\(i = \sqrt{-1}\)[/tex].
[tex]\[
i^2 = (\sqrt{-1})^2
\][/tex]
3. Simplify the right-hand side:
When you square the square root of a number, you get the original number back. Therefore,
[tex]\[
i^2 = -1
\][/tex]
So, the value of [tex]\(i^2\)[/tex] is
[tex]\[
i^2 = -1
\][/tex]
Thus, [tex]\(i^2 = -1\)[/tex] is the final answer.
