Simplify (-2+5i)(-1+4i)

$(- 2 + 5 i) (- 1 + 4 i)$

Step 1

Expand $(- 2 + 5 i) (- 1 + 4 i)$ using the FOIL Method.

Apply the distributive property.

$- 2 (- 1 + 4 i) + 5 i (- 1 + 4 i)$

Apply the distributive property.

$- 2 \cdot - 1 - 2 (4 i) + 5 i (- 1 + 4 i)$

Apply the distributive property.

$- 2 \cdot - 1 - 2 (4 i) + 5 i \cdot - 1 + 5 i (4 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 2$ by $- 1$ .

$2 - 2 (4 i) + 5 i \cdot - 1 + 5 i (4 i)$

Multiply $4$ by $- 2$ .

$2 - 8 i + 5 i \cdot - 1 + 5 i (4 i)$

Multiply $- 1$ by $5$ .

$2 - 8 i - 5 i + 5 i (4 i)$

Multiply $5 i (4 i)$ .

Multiply $4$ by $5$ .

$2 - 8 i - 5 i + 20 i i$

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

$2 - 8 i - 5 i + 20 (i^{1} i)$

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

$2 - 8 i - 5 i + 20 (i^{1} i^{1})$

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

$2 - 8 i - 5 i + 20 i^{1 + 1}$

Add $1$ and $1$ .

$2 - 8 i - 5 i + 20 i^{2}$

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

$2 - 8 i - 5 i + 20 \cdot - 1$

Multiply $20$ by $- 1$ .

$2 - 8 i - 5 i - 20$

Subtract $20$ from $2$ .

$- 18 - 8 i - 5 i$

Subtract $5 i$ from $- 8 i$ .

$- 18 - 13 i$