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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 9$ by $- 9$ .

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

Multiply $- 1$ by $- 9$ .

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

Move $- 9$ to the left of $i$ .

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

Multiply $i (- i)$ .

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

$81 + 9 i - 9 i - (i^{1} i)$

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

$81 + 9 i - 9 i - (i^{1} i^{1})$

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

$81 + 9 i - 9 i - i^{1 + 1}$

Add $1$ and $1$ .

$81 + 9 i - 9 i - i^{2}$

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

$81 + 9 i - 9 i - - 1$

Multiply $- 1$ by $- 1$ .

$81 + 9 i - 9 i + 1$

Add $81$ and $1$ .

$82 + 9 i - 9 i$

Subtract $9 i$ from $9 i$ .

$82 + 0$

Add $82$ and $0$ .

$82$