Let's consider the given information:
1. [tex]\( i = \sqrt{-1} \)[/tex]
To find [tex]\( i^2 \)[/tex]:
2. By definition, squaring both sides of the equation [tex]\( i = \sqrt{-1} \)[/tex] gives us:
[tex]\[ i^2 = (\sqrt{-1})^2 \][/tex]
3. Squaring a square root undoes the square root function, so:
[tex]\[ (\sqrt{-1})^2 = -1 \][/tex]
Therefore, the expression [tex]\( i^2 \)[/tex] evaluates to:
[tex]\[ i^2 = -1 \][/tex]
So, the completed expression is:
[tex]\[ i^2 = -1 \][/tex]
