Question

use the inverse relationship to complete the expression. if $i = \sqrt{-1}$, then $i^2 = \boxed{\quad}$. done

Explanation:

Step1: Recall the definition of \(i\)

Given \(i = \sqrt{-1}\), to find \(i^2\), we square both sides of the equation.

Step2: Square the left and right sides

Squaring the left side gives \(i^2\), and squaring the right side: \((\sqrt{-1})^2\). By the property of square roots, \((\sqrt{a})^2=a\) for \(a\geq0\), here \(a = - 1\) (in the context of imaginary numbers), so \((\sqrt{-1})^2=-1\). So \(i^2=-1\).

Answer:

\(-1\)