Question

use the imaginary number i to rewrite the expre all radicals.
7 + √(-4)

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 \(\sqrt{-4}\)

For \(\sqrt{-4}\), we can split the square root: \(\sqrt{-4}=\sqrt{4\times(-1)}=\sqrt{4}\times\sqrt{-1}\). Since \(\sqrt{4} = 2\) and \(\sqrt{-1}=i\), then \(\sqrt{-4}=2i\).

Step3: Substitute back into the expression

The original expression is \(7+\sqrt{-4}\). Substituting \(\sqrt{-4}=2i\) into it, we get \(7 + 2i\).

Answer:

\(7 + 2i\)