Question

use the imaginary number $i$ to rewrite the expression below as a complex number. simplify all radicals. $-\sqrt{-32}$

Explanation:

Step1: Rewrite negative radicand

$-\sqrt{-32} = -\sqrt{32 \times (-1)}$

Step2: Separate imaginary unit

$= -\sqrt{32} \times \sqrt{-1}$

Step3: Simplify $\sqrt{32}$ and substitute $i=\sqrt{-1}$

$\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}$, so $-4\sqrt{2}i$

Answer:

$-4\sqrt{2}i$