Find the Complex Conjugate square root of -12

$\sqrt{- 12}$

Step 1

Rewrite $- 12$ as $- 1 (12)$ .

$\sqrt{- 1 (12)}$

Step 2

Rewrite $\sqrt{- 1 (12)}$ as $\sqrt{- 1} \cdot \sqrt{12}$ .

$\sqrt{- 1} \cdot \sqrt{12}$

Step 3

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

$i \cdot \sqrt{12}$

Step 4

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$i \cdot \sqrt{4 (3)}$

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

$i \cdot \sqrt{2^{2} \cdot 3}$

Step 5

Pull terms out from under the radical.

$i \cdot (2 \sqrt{3})$

Step 6

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

$2 i \sqrt{3}$

Step 7

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

$- 2 i \sqrt{3}$