Algebra Examples

$- 8 + \sqrt{- 25}$

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

$- 8 + i \cdot 5$

Step 1.6

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

$- 8 + 5 i$

Step 2

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

$- 8 - 5 i$