Question

use the imaginary number i to rewrite the expression below as a complex number. simplify all radicals. -9 - √(-58)

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 term \(\sqrt{-58}\), we have:
\(\sqrt{-58}=\sqrt{58\times(-1)}=\sqrt{58}\times\sqrt{-1}\)

Step2: Substitute \(i\) into the expression

Since \(\sqrt{-1} = i\), then \(\sqrt{-58}=\sqrt{58}i\). Now substitute this back into the original expression \(-9-\sqrt{-58}\):
\(-9 - \sqrt{58}i\)

Answer:

\(-9 - \sqrt{58}i\)