Simplify (-2+i)(-2-i)

$(- 2 + i) (- 2 - i)$

Step 1

Expand $(- 2 + i) (- 2 - i)$ using the FOIL Method.

Apply the distributive property.

$- 2 (- 2 - i) + i (- 2 - i)$

Apply the distributive property.

$- 2 \cdot - 2 - 2 (- i) + i (- 2 - i)$

Apply the distributive property.

$- 2 \cdot - 2 - 2 (- i) + i \cdot - 2 + i (- i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 2$ by $- 2$ .

$4 - 2 (- i) + i \cdot - 2 + i (- i)$

Multiply $- 1$ by $- 2$ .

$4 + 2 i + i \cdot - 2 + i (- i)$

Move $- 2$ to the left of $i$ .

$4 + 2 i - 2 \cdot i + i (- i)$

Multiply $i (- i)$ .

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

$4 + 2 i - 2 i - (i^{1} i)$

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

$4 + 2 i - 2 i - (i^{1} i^{1})$

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

$4 + 2 i - 2 i - i^{1 + 1}$

Add $1$ and $1$ .

$4 + 2 i - 2 i - i^{2}$

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

$4 + 2 i - 2 i - - 1$

Multiply $- 1$ by $- 1$ .

$4 + 2 i - 2 i + 1$

Add $4$ and $1$ .

$5 + 2 i - 2 i$

Subtract $2 i$ from $2 i$ .

$5 + 0$

Add $5$ and $0$ .

$5$