Question

use the imaginary number i to rewrite the expression below as a complex number. simplify all radicals.
$-sqrt{-47}$

Explanation:

Step1: Recall the definition of \(i\)

We know that \(i = \sqrt{-1}\), so we can rewrite \(\sqrt{-a}\) (where \(a>0\)) as \(\sqrt{a}\cdot\sqrt{-1}=\sqrt{a}i\).
For the expression \(-\sqrt{-47}\), we first handle the square root of the negative number.

Step2: Rewrite the square root

Using the property \(\sqrt{-47}=\sqrt{47\times(-1)}=\sqrt{47}\times\sqrt{-1}\). Since \(\sqrt{-1} = i\), we have \(\sqrt{-47}=\sqrt{47}i\).
Then, applying the negative sign in front, we get \(-\sqrt{-47}=-\sqrt{47}i\).

Answer:

\(-i\sqrt{47}\)