Evaluate (4-i square root of 2)-(3+i square root of 2)+8i

$(4 - i \sqrt{2}) - (3 + i \sqrt{2}) + 8 i$

Simplify each term.

Apply the distributive property.

$4 - i \sqrt{2} - 1 \cdot 3 - (i \sqrt{2}) + 8 i$

Multiply $- 1$ by $3$ .

$4 - i \sqrt{2} - 3 - i \sqrt{2} + 8 i$

Simplify by adding terms.

Subtract $3$ from $4$ .

$- i \sqrt{2} + 1 - i \sqrt{2} + 8 i$

Subtract $i \sqrt{2}$ from $- i \sqrt{2}$ .

$- 2 i \sqrt{2} + 1 + 8 i$

Reorder $- 2 i \sqrt{2}$ and $1$ .

$1 - 2 i \sqrt{2} + 8 i$