Simplify (9-2i)(7+6i)

$(9 - 2 i) (7 + 6 i)$

Step 1

Expand $(9 - 2 i) (7 + 6 i)$ using the FOIL Method.

Apply the distributive property.

$9 (7 + 6 i) - 2 i (7 + 6 i)$

Apply the distributive property.

$9 \cdot 7 + 9 (6 i) - 2 i (7 + 6 i)$

Apply the distributive property.

$9 \cdot 7 + 9 (6 i) - 2 i \cdot 7 - 2 i (6 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $9$ by $7$ .

$63 + 9 (6 i) - 2 i \cdot 7 - 2 i (6 i)$

Multiply $6$ by $9$ .

$63 + 54 i - 2 i \cdot 7 - 2 i (6 i)$

Multiply $7$ by $- 2$ .

$63 + 54 i - 14 i - 2 i (6 i)$

Multiply $- 2 i (6 i)$ .

Multiply $6$ by $- 2$ .

$63 + 54 i - 14 i - 12 i i$

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

$63 + 54 i - 14 i - 12 (i^{1} i)$

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

$63 + 54 i - 14 i - 12 (i^{1} i^{1})$

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

$63 + 54 i - 14 i - 12 i^{1 + 1}$

Add $1$ and $1$ .

$63 + 54 i - 14 i - 12 i^{2}$

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

$63 + 54 i - 14 i - 12 \cdot - 1$

Multiply $- 12$ by $- 1$ .

$63 + 54 i - 14 i + 12$

Add $63$ and $12$ .

$75 + 54 i - 14 i$

Subtract $14 i$ from $54 i$ .

$75 + 40 i$