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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $9$ by $9$ .

$81 + 9 (- 6 i) + 6 i \cdot 9 + 6 i (- 6 i)$

Multiply $- 6$ by $9$ .

$81 - 54 i + 6 i \cdot 9 + 6 i (- 6 i)$

Multiply $9$ by $6$ .

$81 - 54 i + 54 i + 6 i (- 6 i)$

Multiply $6 i (- 6 i)$ .

Multiply $- 6$ by $6$ .

$81 - 54 i + 54 i - 36 i i$

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

$81 - 54 i + 54 i - 36 (i^{1} i)$

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

$81 - 54 i + 54 i - 36 (i^{1} i^{1})$

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

$81 - 54 i + 54 i - 36 i^{1 + 1}$

Add $1$ and $1$ .

$81 - 54 i + 54 i - 36 i^{2}$

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

$81 - 54 i + 54 i - 36 \cdot - 1$

Multiply $- 36$ by $- 1$ .

$81 - 54 i + 54 i + 36$

Add $81$ and $36$ .

$117 - 54 i + 54 i$

Add $- 54 i$ and $54 i$ .

$117 + 0$

Add $117$ and $0$ .

$117$