Find the Complex Conjugate square root of -81

$\sqrt{- 81}$

Step 1

Rewrite $- 81$ as $- 1 (81)$ .

$\sqrt{- 1 (81)}$

Step 2

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$\sqrt{- 1} \cdot \sqrt{81}$

Step 3

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

$i \cdot \sqrt{81}$

Step 4

Rewrite $81$ as $9^{2}$ .

$i \cdot \sqrt{9^{2}}$

Step 5

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

$i \cdot 9$

Step 6

Move $9$ to the left of $i$ .

$9 i$

Step 7

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

$- 9 i$