Write in Standard Form (-4-7i)*(3+i)

$(- 4 - 7 i) \cdot (3 + i)$

Expand $(- 4 - 7 i) (3 + i)$ using the FOIL Method.

Apply the distributive property.

$- 4 (3 + i) - 7 i (3 + i)$

Apply the distributive property.

$- 4 \cdot 3 - 4 i - 7 i (3 + i)$

Apply the distributive property.

$- 4 \cdot 3 - 4 i - 7 i \cdot 3 - 7 i i$

Simplify and combine like terms.

Simplify each term.

Multiply $- 4$ by $3$ .

$- 12 - 4 i - 7 i \cdot 3 - 7 i i$

Multiply $3$ by $- 7$ .

$- 12 - 4 i - 21 i - 7 i i$

Multiply $- 7 i i$ .

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

$- 12 - 4 i - 21 i - 7 (i^{1} i)$

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

$- 12 - 4 i - 21 i - 7 (i^{1} i^{1})$

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

$- 12 - 4 i - 21 i - 7 i^{1 + 1}$

Add $1$ and $1$ .

$- 12 - 4 i - 21 i - 7 i^{2}$

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

$- 12 - 4 i - 21 i - 7 \cdot - 1$

Multiply $- 7$ by $- 1$ .

$- 12 - 4 i - 21 i + 7$

Add $- 12$ and $7$ .

$- 5 - 4 i - 21 i$

Subtract $21 i$ from $- 4 i$ .

$- 5 - 25 i$