Simplify (9+7i)(6+3i)

$(9 + 7 i) (6 + 3 i)$

Step 1

Expand $(9 + 7 i) (6 + 3 i)$ using the FOIL Method.

Apply the distributive property.

$9 (6 + 3 i) + 7 i (6 + 3 i)$

Apply the distributive property.

$9 \cdot 6 + 9 (3 i) + 7 i (6 + 3 i)$

Apply the distributive property.

$9 \cdot 6 + 9 (3 i) + 7 i \cdot 6 + 7 i (3 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $9$ by $6$ .

$54 + 9 (3 i) + 7 i \cdot 6 + 7 i (3 i)$

Multiply $3$ by $9$ .

$54 + 27 i + 7 i \cdot 6 + 7 i (3 i)$

Multiply $6$ by $7$ .

$54 + 27 i + 42 i + 7 i (3 i)$

Multiply $7 i (3 i)$ .

Multiply $3$ by $7$ .

$54 + 27 i + 42 i + 21 i i$

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

$54 + 27 i + 42 i + 21 (i^{1} i)$

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

$54 + 27 i + 42 i + 21 (i^{1} i^{1})$

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

$54 + 27 i + 42 i + 21 i^{1 + 1}$

Add $1$ and $1$ .

$54 + 27 i + 42 i + 21 i^{2}$

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

$54 + 27 i + 42 i + 21 \cdot - 1$

Multiply $21$ by $- 1$ .

$54 + 27 i + 42 i - 21$

Subtract $21$ from $54$ .

$33 + 27 i + 42 i$

Add $27 i$ and $42 i$ .

$33 + 69 i$