Simplify (9-4i)(9+4i)

$(9 - 4 i) (9 + 4 i)$

Step 1

Expand $(9 - 4 i) (9 + 4 i)$ using the FOIL Method.

Apply the distributive property.

$9 (9 + 4 i) - 4 i (9 + 4 i)$

Apply the distributive property.

$9 \cdot 9 + 9 (4 i) - 4 i (9 + 4 i)$

Apply the distributive property.

$9 \cdot 9 + 9 (4 i) - 4 i \cdot 9 - 4 i (4 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $9$ by $9$ .

$81 + 9 (4 i) - 4 i \cdot 9 - 4 i (4 i)$

Multiply $4$ by $9$ .

$81 + 36 i - 4 i \cdot 9 - 4 i (4 i)$

Multiply $9$ by $- 4$ .

$81 + 36 i - 36 i - 4 i (4 i)$

Multiply $- 4 i (4 i)$ .

Multiply $4$ by $- 4$ .

$81 + 36 i - 36 i - 16 i i$

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

$81 + 36 i - 36 i - 16 (i^{1} i)$

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

$81 + 36 i - 36 i - 16 (i^{1} i^{1})$

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

$81 + 36 i - 36 i - 16 i^{1 + 1}$

Add $1$ and $1$ .

$81 + 36 i - 36 i - 16 i^{2}$

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

$81 + 36 i - 36 i - 16 \cdot - 1$

Multiply $- 16$ by $- 1$ .

$81 + 36 i - 36 i + 16$

Add $81$ and $16$ .

$97 + 36 i - 36 i$

Subtract $36 i$ from $36 i$ .

$97 + 0$

Add $97$ and $0$ .

$97$