Simplify (2i-3)+(8+ square root of -9)

$(2 i - 3) + (8 + \sqrt{- 9})$

Remove parentheses.

$2 i - 3 + 8 + \sqrt{- 9}$

Simplify each term.

Rewrite $- 9$ as $- 1 (9)$ .

$2 i - 3 + 8 + \sqrt{- 1 (9)}$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$2 i - 3 + 8 + \sqrt{- 1} \cdot \sqrt{9}$

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

$2 i - 3 + 8 + i \cdot \sqrt{9}$

Rewrite $9$ as $3^{2}$ .

$2 i - 3 + 8 + i \cdot \sqrt{3^{2}}$

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

$2 i - 3 + 8 + i \cdot 3$

Move $3$ to the left of $i$ .

$2 i - 3 + 8 + 3 i$

Simplify by adding terms.

Add $2 i$ and $3 i$ .

$- 3 + 8 + 5 i$

Add $- 3$ and $8$ .

$5 + 5 i$