Simplify (-1+i)(-1-i)

$(- 1 + i) (- 1 - i)$

Step 1

Expand $(- 1 + i) (- 1 - i)$ using the FOIL Method.

Apply the distributive property.

$- 1 (- 1 - i) + i (- 1 - i)$

Apply the distributive property.

$- 1 \cdot - 1 - 1 (- i) + i (- 1 - i)$

Apply the distributive property.

$- 1 \cdot - 1 - 1 (- i) + i \cdot - 1 + i (- i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 1$ by $- 1$ .

$1 - 1 (- i) + i \cdot - 1 + i (- i)$

Multiply $- 1$ by $- 1$ .

$1 + 1 i + i \cdot - 1 + i (- i)$

Multiply $i$ by $1$ .

$1 + i + i \cdot - 1 + i (- i)$

Move $- 1$ to the left of $i$ .

$1 + i - 1 \cdot i + i (- i)$

Rewrite $- 1 i$ as $- i$ .

$1 + i - i + i (- i)$

Multiply $i (- i)$ .

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

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

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

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

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

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

Add $1$ and $1$ .

$1 + i - i - i^{2}$

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

$1 + i - i - - 1$

Multiply $- 1$ by $- 1$ .

$1 + i - i + 1$

Add $1$ and $1$ .

$2 + i - i$

Subtract $i$ from $i$ .

$2 + 0$

Add $2$ and $0$ .

$2$