Simplify (3+i square root of 64)-(2+i square root of 4)

$(3 + i \sqrt{64}) - (2 + i \sqrt{4})$

Step 1

Simplify each term.

Rewrite $64$ as $8^{2}$ .

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

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

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

Move $8$ to the left of $i$ .

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

Simplify each term.

Rewrite $4$ as $2^{2}$ .

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

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

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

Move $2$ to the left of $i$ .

$3 + 8 i - (2 + 2 i)$

Apply the distributive property.

$3 + 8 i - 1 \cdot 2 - (2 i)$

Multiply $- 1$ by $2$ .

$3 + 8 i - 2 - (2 i)$

Multiply $2$ by $- 1$ .

$3 + 8 i - 2 - 2 i$

Step 2

Simplify by adding terms.

Subtract $2$ from $3$ .

$1 + 8 i - 2 i$

Subtract $2 i$ from $8 i$ .

$1 + 6 i$