Simplify (-2-2i)(-4+6i)

$(- 2 - 2 i) (- 4 + 6 i)$

Step 1

Expand $(- 2 - 2 i) (- 4 + 6 i)$ using the FOIL Method.

Apply the distributive property.

$- 2 (- 4 + 6 i) - 2 i (- 4 + 6 i)$

Apply the distributive property.

$- 2 \cdot - 4 - 2 (6 i) - 2 i (- 4 + 6 i)$

Apply the distributive property.

$- 2 \cdot - 4 - 2 (6 i) - 2 i \cdot - 4 - 2 i (6 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 2$ by $- 4$ .

$8 - 2 (6 i) - 2 i \cdot - 4 - 2 i (6 i)$

Multiply $6$ by $- 2$ .

$8 - 12 i - 2 i \cdot - 4 - 2 i (6 i)$

Multiply $- 4$ by $- 2$ .

$8 - 12 i + 8 i - 2 i (6 i)$

Multiply $- 2 i (6 i)$ .

Multiply $6$ by $- 2$ .

$8 - 12 i + 8 i - 12 i i$

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

$8 - 12 i + 8 i - 12 (i^{1} i)$

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

$8 - 12 i + 8 i - 12 (i^{1} i^{1})$

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

$8 - 12 i + 8 i - 12 i^{1 + 1}$

Add $1$ and $1$ .

$8 - 12 i + 8 i - 12 i^{2}$

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

$8 - 12 i + 8 i - 12 \cdot - 1$

Multiply $- 12$ by $- 1$ .

$8 - 12 i + 8 i + 12$

Add $8$ and $12$ .

$20 - 12 i + 8 i$

Add $- 12 i$ and $8 i$ .

$20 - 4 i$