Find the Complex Conjugate -8+ square root of -25

$- 8 + \sqrt{- 25}$

Step 1

Simplify each term.

Rewrite $- 25$ as $- 1 (25)$ .

$- 8 + \sqrt{- 1 (25)}$

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$- 8 + \sqrt{- 1} \cdot \sqrt{25}$

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

$- 8 + i \cdot \sqrt{25}$

Rewrite $25$ as $5^{2}$ .

$- 8 + i \cdot \sqrt{5^{2}}$

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

$- 8 + i \cdot 5$

Move $5$ to the left of $i$ .

$- 8 + 5 i$

Step 2

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

$- 8 - 5 i$