Simplify 4i+(8-3i)-(12+ square root of -25)

$4 i + (8 - 3 i) - (12 + \sqrt{- 25})$

Step 1

Remove parentheses.

$4 i + 8 - 3 i - (12 + \sqrt{- 25})$

Step 2

Simplify each term.

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

$4 i + 8 - 3 i - (12 + \sqrt{- 1 (25)})$

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

$4 i + 8 - 3 i - (12 + \sqrt{- 1} \cdot \sqrt{25})$

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

$4 i + 8 - 3 i - (12 + i \cdot \sqrt{25})$

Simplify each term.

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

$4 i + 8 - 3 i - (12 + i \cdot \sqrt{5^{2}})$

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

$4 i + 8 - 3 i - (12 + i \cdot 5)$

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

$4 i + 8 - 3 i - (12 + 5 i)$

Apply the distributive property.

$4 i + 8 - 3 i - 1 \cdot 12 - (5 i)$

Multiply $- 1$ by $12$ .

$4 i + 8 - 3 i - 12 - (5 i)$

Multiply $5$ by $- 1$ .

$4 i + 8 - 3 i - 12 - 5 i$

Step 3

Simplify by adding terms.

Subtract $3 i$ from $4 i$ .

$8 + i - 12 - 5 i$

Subtract $12$ from $8$ .

$- 4 + i - 5 i$

Subtract $5 i$ from $i$ .

$- 4 - 4 i$