Simplify (9i+3 square root of -3)+(2i-7 square root of -3)

$(9 i + 3 \sqrt{- 3}) + (2 i - 7 \sqrt{- 3})$

Step 1

Remove parentheses.

$9 i + 3 \sqrt{- 3} + 2 i - 7 \sqrt{- 3}$

Step 2

Simplify each term.

Rewrite $- 3$ as $- 1 (3)$ .

$9 i + 3 \sqrt{- 1 (3)} + 2 i - 7 \sqrt{- 3}$

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$9 i + 3 (\sqrt{- 1} \cdot \sqrt{3}) + 2 i - 7 \sqrt{- 3}$

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

$9 i + 3 (i \cdot \sqrt{3}) + 2 i - 7 \sqrt{- 3}$

Rewrite $- 3$ as $- 1 (3)$ .

$9 i + 3 i \sqrt{3} + 2 i - 7 \sqrt{- 1 (3)}$

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$9 i + 3 i \sqrt{3} + 2 i - 7 (\sqrt{- 1} \cdot \sqrt{3})$

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

$9 i + 3 i \sqrt{3} + 2 i - 7 i \sqrt{3}$

Step 3

Simplify by adding terms.

Add $9 i$ and $2 i$ .

$3 i \sqrt{3} + 11 i - 7 i \sqrt{3}$

Subtract $7 i \sqrt{3}$ from $3 i \sqrt{3}$ .

$- 4 i \sqrt{3} + 11 i$