Question

use the imaginary number $i$ to rewrite the expression below as a complex number. simplify all radicals.
$2 + \sqrt{-12}$

Explanation:

Step1: Rewrite negative radical with $i$

$\sqrt{-12} = \sqrt{12} \cdot \sqrt{-1} = \sqrt{12}i$

Step2: Simplify the radical

$\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}$

Step3: Substitute back to expression

$2 + 2\sqrt{3}i$

Answer:

$2 + 2\sqrt{3}i$