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Use the inverse relation:

If [tex]i=\sqrt{-1}[/tex], then [tex]i^2=[/tex] [tex]\[\ \][/tex]

Sagot :

GinnyAnswer
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.
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