Simplify (5- square root of -49)+(2+3i)

$(5 - \sqrt{- 49}) + (2 + 3 i)$

Step 1

Remove parentheses.

$5 - \sqrt{- 49} + 2 + 3 i$

Step 2

Simplify each term.

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

$5 - \sqrt{- 1 (49)} + 2 + 3 i$

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

$5 - (\sqrt{- 1} \cdot \sqrt{49}) + 2 + 3 i$

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

$5 - (i \cdot \sqrt{49}) + 2 + 3 i$

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

$5 - (i \cdot \sqrt{7^{2}}) + 2 + 3 i$

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

$5 - (i \cdot 7) + 2 + 3 i$

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

$5 - (7 \cdot i) + 2 + 3 i$

Multiply $7$ by $- 1$ .

$5 - 7 i + 2 + 3 i$

Step 3

Simplify by adding terms.

Add $5$ and $2$ .

$7 - 7 i + 3 i$

Add $- 7 i$ and $3 i$ .

$7 - 4 i$