Simplify (8-6i)(-4-4i)

$(8 - 6 i) (- 4 - 4 i)$

Step 1

Expand $(8 - 6 i) (- 4 - 4 i)$ using the FOIL Method.

Apply the distributive property.

$8 (- 4 - 4 i) - 6 i (- 4 - 4 i)$

Apply the distributive property.

$8 \cdot - 4 + 8 (- 4 i) - 6 i (- 4 - 4 i)$

Apply the distributive property.

$8 \cdot - 4 + 8 (- 4 i) - 6 i \cdot - 4 - 6 i (- 4 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $- 4$ .

$- 32 + 8 (- 4 i) - 6 i \cdot - 4 - 6 i (- 4 i)$

Multiply $- 4$ by $8$ .

$- 32 - 32 i - 6 i \cdot - 4 - 6 i (- 4 i)$

Multiply $- 4$ by $- 6$ .

$- 32 - 32 i + 24 i - 6 i (- 4 i)$

Multiply $- 6 i (- 4 i)$ .

Multiply $- 4$ by $- 6$ .

$- 32 - 32 i + 24 i + 24 i i$

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

$- 32 - 32 i + 24 i + 24 (i^{1} i)$

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

$- 32 - 32 i + 24 i + 24 (i^{1} i^{1})$

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

$- 32 - 32 i + 24 i + 24 i^{1 + 1}$

Add $1$ and $1$ .

$- 32 - 32 i + 24 i + 24 i^{2}$

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

$- 32 - 32 i + 24 i + 24 \cdot - 1$

Multiply $24$ by $- 1$ .

$- 32 - 32 i + 24 i - 24$

Subtract $24$ from $- 32$ .

$- 56 - 32 i + 24 i$

Add $- 32 i$ and $24 i$ .

$- 56 - 8 i$