Simplify (5+ square root of -36)-(-4- square root of -49)

$(5 + \sqrt{- 36}) - (- 4 - \sqrt{- 49})$

Step 1

Simplify each term.

Rewrite $- 36$ as $- 1 (36)$ .

$5 + \sqrt{- 1 (36)} - (- 4 - \sqrt{- 49})$

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$5 + \sqrt{- 1} \cdot \sqrt{36} - (- 4 - \sqrt{- 49})$

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

$5 + i \cdot \sqrt{36} - (- 4 - \sqrt{- 49})$

Rewrite $36$ as $6^{2}$ .

$5 + i \cdot \sqrt{6^{2}} - (- 4 - \sqrt{- 49})$

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

$5 + i \cdot 6 - (- 4 - \sqrt{- 49})$

Move $6$ to the left of $i$ .

$5 + 6 \cdot i - (- 4 - \sqrt{- 49})$

Rewrite $- 49$ as $- 1 (49)$ .

$5 + 6 i - (- 4 - \sqrt{- 1 (49)})$

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$5 + 6 i - (- 4 - (\sqrt{- 1} \cdot \sqrt{49}))$

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

$5 + 6 i - (- 4 - (i \cdot \sqrt{49}))$

Simplify each term.

Rewrite $49$ as $7^{2}$ .

$5 + 6 i - (- 4 - (i \cdot \sqrt{7^{2}}))$

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

$5 + 6 i - (- 4 - (i \cdot 7))$

Move $7$ to the left of $i$ .

$5 + 6 i - (- 4 - (7 \cdot i))$

Multiply $7$ by $- 1$ .

$5 + 6 i - (- 4 - 7 i)$

Apply the distributive property.

$5 + 6 i - - 4 - (- 7 i)$

Multiply $- 1$ by $- 4$ .

$5 + 6 i + 4 - (- 7 i)$

Multiply $- 7$ by $- 1$ .

$5 + 6 i + 4 + 7 i$

Step 2

Simplify by adding terms.

Add $5$ and $4$ .

$9 + 6 i + 7 i$

Add $6 i$ and $7 i$ .

$9 + 13 i$