Question

use the imaginary number i to rewrite the expression all radicals.
-8 + √(-100)
-8+10i

Explanation:

Step1: Recall the definition of \(i\)

The imaginary unit \(i\) is defined as \(i = \sqrt{-1}\), so we can rewrite \(\sqrt{-a}\) (where \(a>0\)) as \(\sqrt{a}\cdot\sqrt{-1}=\sqrt{a}i\).

Step2: Rewrite \(\sqrt{-100}\)

For \(\sqrt{-100}\), we can split the square root: \(\sqrt{-100}=\sqrt{100\times(-1)}=\sqrt{100}\times\sqrt{-1}\). Since \(\sqrt{100} = 10\) and \(\sqrt{-1}=i\), this becomes \(10i\).

Step3: Substitute back into the expression

The original expression is \(-8+\sqrt{-100}\). Substituting \(\sqrt{-100}=10i\) into it, we get \(-8 + 10i\).

Answer:

\(-8 + 10i\)