Question

use the imaginary number $i$ to rewrite the expression below as a complex number. simplify all radicals.
$-17 + \sqrt{-99}$

Explanation:

Step1: Rewrite sqrt of negative number

$\sqrt{-99} = \sqrt{99 \times (-1)} = \sqrt{99} \times \sqrt{-1}$

Step2: Substitute $i = \sqrt{-1}$

$\sqrt{99} \times i = \sqrt{9 \times 11} \times i$

Step3: Simplify the radical

$\sqrt{9} \times \sqrt{11} \times i = 3\sqrt{11}i$

Step4: Combine with real part

$-17 + 3\sqrt{11}i$

Answer:

$-17 + 3\sqrt{11}i$