Question

use the imaginary number i to rewrite the expression below as a complex number. simplify all radicals. 8 - √(-7)

Explanation:

Step1: Recall the definition of \(i\)

We know that \(i = \sqrt{-1}\), so we can rewrite \(\sqrt{-7}\) by factoring out \(\sqrt{-1}\).
\(\sqrt{-7}=\sqrt{7\times(-1)}=\sqrt{7}\times\sqrt{-1}\)

Step2: Substitute \(i\) for \(\sqrt{-1}\)

Since \(\sqrt{-1} = i\), then \(\sqrt{7}\times\sqrt{-1}=\sqrt{7}i\).

Step3: Rewrite the original expression

The original expression is \(8-\sqrt{-7}\), substituting the simplified radical, we get \(8 - \sqrt{7}i\).

Answer:

\(8 - \sqrt{7}i\)