Question

write in terms of i. simplify your answer as much as possible. \sqrt{-37}

Explanation:

Step1: Recall the definition of imaginary unit

We know that \(i = \sqrt{-1}\), so we can rewrite \(\sqrt{-37}\) as \(\sqrt{37\times(-1)}\).

Step2: Use the property of square roots

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\), here we extend it to complex numbers), we have \(\sqrt{37\times(-1)}=\sqrt{37}\times\sqrt{-1}\).

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

Since \(\sqrt{-1}=i\), then \(\sqrt{37}\times\sqrt{-1}=\sqrt{37}i\).

Answer:

\(\sqrt{37}i\)