Question

use the imaginary number i to rewrite the expression below as a complex number. simplify all radicals.
12 + \sqrt{-17}

Explanation:

Step1: Recall the definition of \(i\)

We know that \(i = \sqrt{-1}\), so we can rewrite \(\sqrt{-17}\) by factoring out \(\sqrt{-1}\).
\(\sqrt{-17}=\sqrt{17\times(-1)}=\sqrt{17}\times\sqrt{-1}\)

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

Since \(\sqrt{-1} = i\), we substitute that into the expression. So \(\sqrt{17}\times\sqrt{-1}=\sqrt{17}i\)

Step3: Rewrite the original expression

The original expression is \(12+\sqrt{-17}\), substituting the simplified radical we get \(12 + \sqrt{17}i\)

Answer:

\(12 + \sqrt{17}i\)