Question

simplify.
$i^2$
write your answer in the form $a + bi$.

Explanation:

Step1: Recall the definition of the imaginary unit \(i\)

The imaginary unit \(i\) is defined as \(i = \sqrt{-1}\).

Step2: Square both sides of the definition

Squaring both sides, we get \(i^2 = (\sqrt{-1})^2\). By the property of square roots, \((\sqrt{x})^2 = x\) for \(x\geq0\), so here \(i^2 = -1\).

Step3: Write in the form \(a + bi\)

We can write \(-1\) as \(-1 + 0i\), where \(a = -1\) and \(b = 0\).

Answer:

\(-1 + 0i\) (or simply \(-1\) since the \(0i\) term is often omitted, but in the strict form \(a + bi\), it is \(-1 + 0i\))