Write in Standard Form (-11+i)(-11-i)

$(- 11 + i) (- 11 - i)$

Step 1

Expand $(- 11 + i) (- 11 - i)$ using the FOIL Method.

Apply the distributive property.

$- 11 (- 11 - i) + i (- 11 - i)$

Apply the distributive property.

$- 11 \cdot - 11 - 11 (- i) + i (- 11 - i)$

Apply the distributive property.

$- 11 \cdot - 11 - 11 (- i) + i \cdot - 11 + i (- i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 11$ by $- 11$ .

$121 - 11 (- i) + i \cdot - 11 + i (- i)$

Multiply $- 1$ by $- 11$ .

$121 + 11 i + i \cdot - 11 + i (- i)$

Move $- 11$ to the left of $i$ .

$121 + 11 i - 11 \cdot i + i (- i)$

Multiply $i (- i)$ .

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

$121 + 11 i - 11 i - (i^{1} i)$

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

$121 + 11 i - 11 i - (i^{1} i^{1})$

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

$121 + 11 i - 11 i - i^{1 + 1}$

Add $1$ and $1$ .

$121 + 11 i - 11 i - i^{2}$

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

$121 + 11 i - 11 i - - 1$

Multiply $- 1$ by $- 1$ .

$121 + 11 i - 11 i + 1$

Add $121$ and $1$ .

$122 + 11 i - 11 i$

Subtract $11 i$ from $11 i$ .

$122 + 0$

Add $122$ and $0$ .

$122$