Simplify (-5+ square root of -25)-(2- square root of -16)

$(- 5 + \sqrt{- 25}) - (2 - \sqrt{- 16})$

Step 1

Simplify each term.

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

$- 5 + \sqrt{- 1 (25)} - (2 - \sqrt{- 16})$

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

$- 5 + \sqrt{- 1} \cdot \sqrt{25} - (2 - \sqrt{- 16})$

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

$- 5 + i \cdot \sqrt{25} - (2 - \sqrt{- 16})$

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

$- 5 + i \cdot \sqrt{5^{2}} - (2 - \sqrt{- 16})$

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

$- 5 + i \cdot 5 - (2 - \sqrt{- 16})$

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

$- 5 + 5 \cdot i - (2 - \sqrt{- 16})$

Rewrite $- 16$ as $- 1 (16)$ .

$- 5 + 5 i - (2 - \sqrt{- 1 (16)})$

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$- 5 + 5 i - (2 - (\sqrt{- 1} \cdot \sqrt{16}))$

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

$- 5 + 5 i - (2 - (i \cdot \sqrt{16}))$

Simplify each term.

Rewrite $16$ as $4^{2}$ .

$- 5 + 5 i - (2 - (i \cdot \sqrt{4^{2}}))$

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

$- 5 + 5 i - (2 - (i \cdot 4))$

Move $4$ to the left of $i$ .

$- 5 + 5 i - (2 - (4 \cdot i))$

Multiply $4$ by $- 1$ .

$- 5 + 5 i - (2 - 4 i)$

Apply the distributive property.

$- 5 + 5 i - 1 \cdot 2 - (- 4 i)$

Multiply $- 1$ by $2$ .

$- 5 + 5 i - 2 - (- 4 i)$

Multiply $- 4$ by $- 1$ .

$- 5 + 5 i - 2 + 4 i$

Step 2

Simplify by adding terms.

Subtract $2$ from $- 5$ .

$- 7 + 5 i + 4 i$

Add $5 i$ and $4 i$ .

$- 7 + 9 i$