Simplify (-1-5i)(-1+5i)

$(- 1 - 5 i) (- 1 + 5 i)$

Step 1

Expand $(- 1 - 5 i) (- 1 + 5 i)$ using the FOIL Method.

Apply the distributive property.

$- 1 (- 1 + 5 i) - 5 i (- 1 + 5 i)$

Apply the distributive property.

$- 1 \cdot - 1 - 1 (5 i) - 5 i (- 1 + 5 i)$

Apply the distributive property.

$- 1 \cdot - 1 - 1 (5 i) - 5 i \cdot - 1 - 5 i (5 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 1$ by $- 1$ .

$1 - 1 (5 i) - 5 i \cdot - 1 - 5 i (5 i)$

Multiply $5$ by $- 1$ .

$1 - 5 i - 5 i \cdot - 1 - 5 i (5 i)$

Multiply $- 1$ by $- 5$ .

$1 - 5 i + 5 i - 5 i (5 i)$

Multiply $- 5 i (5 i)$ .

Multiply $5$ by $- 5$ .

$1 - 5 i + 5 i - 25 i i$

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

$1 - 5 i + 5 i - 25 (i^{1} i)$

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

$1 - 5 i + 5 i - 25 (i^{1} i^{1})$

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

$1 - 5 i + 5 i - 25 i^{1 + 1}$

Add $1$ and $1$ .

$1 - 5 i + 5 i - 25 i^{2}$

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

$1 - 5 i + 5 i - 25 \cdot - 1$

Multiply $- 25$ by $- 1$ .

$1 - 5 i + 5 i + 25$

Add $1$ and $25$ .

$26 - 5 i + 5 i$

Add $- 5 i$ and $5 i$ .

$26 + 0$

Add $26$ and $0$ .

$26$