Find the Complex Conjugate square root of -4

$\sqrt{- 4}$

Rewrite $- 4$ as $- 1 (4)$ .

$\sqrt{- 1 (4)}$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$\sqrt{- 1} \cdot \sqrt{4}$

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

$i \cdot \sqrt{4}$

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

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

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

$i \cdot 2$

Move $2$ to the left of $i$ .

$2 i$

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

$- 2 i$