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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 4$ by $- 4$ .

$16 - 4 (- 7 i) + 7 i \cdot - 4 + 7 i (- 7 i)$

Multiply $- 7$ by $- 4$ .

$16 + 28 i + 7 i \cdot - 4 + 7 i (- 7 i)$

Multiply $- 4$ by $7$ .

$16 + 28 i - 28 i + 7 i (- 7 i)$

Multiply $7 i (- 7 i)$ .

Multiply $- 7$ by $7$ .

$16 + 28 i - 28 i - 49 i i$

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

$16 + 28 i - 28 i - 49 (i^{1} i)$

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

$16 + 28 i - 28 i - 49 (i^{1} i^{1})$

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

$16 + 28 i - 28 i - 49 i^{1 + 1}$

Add $1$ and $1$ .

$16 + 28 i - 28 i - 49 i^{2}$

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

$16 + 28 i - 28 i - 49 \cdot - 1$

Multiply $- 49$ by $- 1$ .

$16 + 28 i - 28 i + 49$

Add $16$ and $49$ .

$65 + 28 i - 28 i$

Subtract $28 i$ from $28 i$ .

$65 + 0$

Add $65$ and $0$ .

$65$