Find the Complex Conjugate square root of -16

$\sqrt{- 16}$

Rewrite $- 16$ as $- 1 (16)$ .

$\sqrt{- 1 (16)}$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$\sqrt{- 1} \cdot \sqrt{16}$

Rewrite $\sqrt{- 1}$ as $i$ .

$i \cdot \sqrt{16}$

Rewrite $16$ as $4^{2}$ .

$i \cdot \sqrt{4^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$i \cdot 4$

Move $4$ to the left of $i$ .

$4 i$

To find the complex conjugate, negate the term with $i$ .

$- 4 i$