Simplify (-8+4i)(-5-7i)

$(- 8 + 4 i) (- 5 - 7 i)$

Step 1

Expand $(- 8 + 4 i) (- 5 - 7 i)$ using the FOIL Method.

Apply the distributive property.

$- 8 (- 5 - 7 i) + 4 i (- 5 - 7 i)$

Apply the distributive property.

$- 8 \cdot - 5 - 8 (- 7 i) + 4 i (- 5 - 7 i)$

Apply the distributive property.

$- 8 \cdot - 5 - 8 (- 7 i) + 4 i \cdot - 5 + 4 i (- 7 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 8$ by $- 5$ .

$40 - 8 (- 7 i) + 4 i \cdot - 5 + 4 i (- 7 i)$

Multiply $- 7$ by $- 8$ .

$40 + 56 i + 4 i \cdot - 5 + 4 i (- 7 i)$

Multiply $- 5$ by $4$ .

$40 + 56 i - 20 i + 4 i (- 7 i)$

Multiply $4 i (- 7 i)$ .

Multiply $- 7$ by $4$ .

$40 + 56 i - 20 i - 28 i i$

Raise $i$ to the power of $1$ .

$40 + 56 i - 20 i - 28 (i^{1} i)$

Raise $i$ to the power of $1$ .

$40 + 56 i - 20 i - 28 (i^{1} i^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$40 + 56 i - 20 i - 28 i^{1 + 1}$

Add $1$ and $1$ .

$40 + 56 i - 20 i - 28 i^{2}$

Rewrite $i^{2}$ as $- 1$ .

$40 + 56 i - 20 i - 28 \cdot - 1$

Multiply $- 28$ by $- 1$ .

$40 + 56 i - 20 i + 28$

Add $40$ and $28$ .

$68 + 56 i - 20 i$

Subtract $20 i$ from $56 i$ .

$68 + 36 i$