Simplify (6-8i)(2+7i)

$(6 - 8 i) (2 + 7 i)$

Step 1

Expand $(6 - 8 i) (2 + 7 i)$ using the FOIL Method.

Apply the distributive property.

$6 (2 + 7 i) - 8 i (2 + 7 i)$

Apply the distributive property.

$6 \cdot 2 + 6 (7 i) - 8 i (2 + 7 i)$

Apply the distributive property.

$6 \cdot 2 + 6 (7 i) - 8 i \cdot 2 - 8 i (7 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $2$ .

$12 + 6 (7 i) - 8 i \cdot 2 - 8 i (7 i)$

Multiply $7$ by $6$ .

$12 + 42 i - 8 i \cdot 2 - 8 i (7 i)$

Multiply $2$ by $- 8$ .

$12 + 42 i - 16 i - 8 i (7 i)$

Multiply $- 8 i (7 i)$ .

Multiply $7$ by $- 8$ .

$12 + 42 i - 16 i - 56 i i$

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

$12 + 42 i - 16 i - 56 (i^{1} i)$

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

$12 + 42 i - 16 i - 56 (i^{1} i^{1})$

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

$12 + 42 i - 16 i - 56 i^{1 + 1}$

Add $1$ and $1$ .

$12 + 42 i - 16 i - 56 i^{2}$

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

$12 + 42 i - 16 i - 56 \cdot - 1$

Multiply $- 56$ by $- 1$ .

$12 + 42 i - 16 i + 56$

Add $12$ and $56$ .

$68 + 42 i - 16 i$

Subtract $16 i$ from $42 i$ .

$68 + 26 i$