Question

which of the following is equal to -1? select all that apply.
$i^2$ $i^4$ $i^6$ $i^8$
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Explanation:

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

We know that \(i = \sqrt{-1}\), so by squaring both sides, we get \(i^{2}=(\sqrt{-1})^{2}=- 1\).

Step2: Analyze \(i^{4}\)

We can express \(i^{4}\) as \((i^{2})^{2}\). Since we already know that \(i^{2}=-1\), then \((i^{2})^{2}=(-1)^{2} = 1
eq - 1\).

Step3: Analyze \(i^{6}\)

We can write \(i^{6}\) as \(i^{4}\times i^{2}\). We know \(i^{4} = 1\) (from Step 2) and \(i^{2}=-1\), so \(i^{6}=i^{4}\times i^{2}=1\times(-1)=-1\).

Step4: Analyze \(i^{8}\)

We can express \(i^{8}\) as \((i^{4})^{2}\). Since \(i^{4} = 1\), then \((i^{4})^{2}=1^{2}=1
eq - 1\).

So the expressions equal to \(-1\) are \(i^{2}\) and \(i^{6}\). The original selection had incorrect selections for \(i^{4}\) and \(i^{8}\).

Answer:

The correct options are:

• \(i^{2}\)
• \(i^{6}\)