Question

use the imaginary number $i$ to rewrite the expression below as a complex number. simplify all radicals.
$-sqrt{-52}$

Explanation:

Step1: Rewrite negative radicand

$-\sqrt{-52} = -\sqrt{52 \times (-1)}$

Step2: Separate imaginary unit

$= -\sqrt{52} \times \sqrt{-1}$

Step3: Substitute $i=\sqrt{-1}$

$= -i\sqrt{52}$

Step4: Simplify radical

$\sqrt{52} = \sqrt{4 \times 13} = \sqrt{4}\sqrt{13} = 2\sqrt{13}$

Step5: Substitute simplified radical

$= -i \times 2\sqrt{13}$

Answer:

$-2i\sqrt{13}$