Question

write in terms of i. simplify your answer as mu √-38

Explanation:

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

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

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (for \(a\geq0,b\geq0\), here we extend it to complex numbers)

\(\sqrt{38\times(-1)}=\sqrt{38}\cdot\sqrt{-1}\)

Step3: Substitute \(\sqrt{-1}\) with \(i\)

Since \(\sqrt{-1} = i\), we have \(\sqrt{38}\cdot i\), which is \(i\sqrt{38}\).

Answer:

\(i\sqrt{38}\)