Simplify (7-3i)(8+4i)

$(7 - 3 i) (8 + 4 i)$

Step 1

Expand $(7 - 3 i) (8 + 4 i)$ using the FOIL Method.

Apply the distributive property.

$7 (8 + 4 i) - 3 i (8 + 4 i)$

Apply the distributive property.

$7 \cdot 8 + 7 (4 i) - 3 i (8 + 4 i)$

Apply the distributive property.

$7 \cdot 8 + 7 (4 i) - 3 i \cdot 8 - 3 i (4 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $7$ by $8$ .

$56 + 7 (4 i) - 3 i \cdot 8 - 3 i (4 i)$

Multiply $4$ by $7$ .

$56 + 28 i - 3 i \cdot 8 - 3 i (4 i)$

Multiply $8$ by $- 3$ .

$56 + 28 i - 24 i - 3 i (4 i)$

Multiply $- 3 i (4 i)$ .

Multiply $4$ by $- 3$ .

$56 + 28 i - 24 i - 12 i i$

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

$56 + 28 i - 24 i - 12 (i^{1} i)$

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

$56 + 28 i - 24 i - 12 (i^{1} i^{1})$

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

$56 + 28 i - 24 i - 12 i^{1 + 1}$

Add $1$ and $1$ .

$56 + 28 i - 24 i - 12 i^{2}$

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

$56 + 28 i - 24 i - 12 \cdot - 1$

Multiply $- 12$ by $- 1$ .

$56 + 28 i - 24 i + 12$

Add $56$ and $12$ .

$68 + 28 i - 24 i$

Subtract $24 i$ from $28 i$ .

$68 + 4 i$