Question

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quiz 1
express the radical using the imaginary unit, i.
express your answer in simplified form.
±√(-38) = ±

Explanation:

Step1: Recall the definition of \(i\)

We know that \(i = \sqrt{-1}\), so we can rewrite \(\sqrt{-38}\) as \(\sqrt{38\times(-1)}\).

Step2: Use the property of square roots

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0, b\geq0\), and here we extend it for complex numbers), we have \(\sqrt{38\times(-1)}=\sqrt{38}\times\sqrt{-1}\).

Step3: Substitute \(i\)

Since \(\sqrt{-1} = i\), then \(\sqrt{38}\times\sqrt{-1}=\sqrt{38}i\). And since the original expression has \(\pm\), we get \(\pm\sqrt{-38}=\pm\sqrt{38}i\).

Answer:

\(\sqrt{38}i\)