Simplify (4+2i)(-3-5i)

$(4 + 2 i) (- 3 - 5 i)$

Step 1

Expand $(4 + 2 i) (- 3 - 5 i)$ using the FOIL Method.

Apply the distributive property.

$4 (- 3 - 5 i) + 2 i (- 3 - 5 i)$

Apply the distributive property.

$4 \cdot - 3 + 4 (- 5 i) + 2 i (- 3 - 5 i)$

Apply the distributive property.

$4 \cdot - 3 + 4 (- 5 i) + 2 i \cdot - 3 + 2 i (- 5 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $- 3$ .

$- 12 + 4 (- 5 i) + 2 i \cdot - 3 + 2 i (- 5 i)$

Multiply $- 5$ by $4$ .

$- 12 - 20 i + 2 i \cdot - 3 + 2 i (- 5 i)$

Multiply $- 3$ by $2$ .

$- 12 - 20 i - 6 i + 2 i (- 5 i)$

Multiply $2 i (- 5 i)$ .

Multiply $- 5$ by $2$ .

$- 12 - 20 i - 6 i - 10 i i$

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

$- 12 - 20 i - 6 i - 10 (i^{1} i)$

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

$- 12 - 20 i - 6 i - 10 (i^{1} i^{1})$

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

$- 12 - 20 i - 6 i - 10 i^{1 + 1}$

Add $1$ and $1$ .

$- 12 - 20 i - 6 i - 10 i^{2}$

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

$- 12 - 20 i - 6 i - 10 \cdot - 1$

Multiply $- 10$ by $- 1$ .

$- 12 - 20 i - 6 i + 10$

Add $- 12$ and $10$ .

$- 2 - 20 i - 6 i$

Subtract $6 i$ from $- 20 i$ .

$- 2 - 26 i$