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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $9$ by $9$ .

$81 + 9 (- 7 i) + 7 i \cdot 9 + 7 i (- 7 i)$

Multiply $- 7$ by $9$ .

$81 - 63 i + 7 i \cdot 9 + 7 i (- 7 i)$

Multiply $9$ by $7$ .

$81 - 63 i + 63 i + 7 i (- 7 i)$

Multiply $7 i (- 7 i)$ .

Multiply $- 7$ by $7$ .

$81 - 63 i + 63 i - 49 i i$

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

$81 - 63 i + 63 i - 49 (i^{1} i)$

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

$81 - 63 i + 63 i - 49 (i^{1} i^{1})$

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

$81 - 63 i + 63 i - 49 i^{1 + 1}$

Add $1$ and $1$ .

$81 - 63 i + 63 i - 49 i^{2}$

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

$81 - 63 i + 63 i - 49 \cdot - 1$

Multiply $- 49$ by $- 1$ .

$81 - 63 i + 63 i + 49$

Add $81$ and $49$ .

$130 - 63 i + 63 i$

Add $- 63 i$ and $63 i$ .

$130 + 0$

Add $130$ and $0$ .

$130$