Simplify (1+8i)(-3-2i)

$(1 + 8 i) (- 3 - 2 i)$

Step 1

Expand $(1 + 8 i) (- 3 - 2 i)$ using the FOIL Method.

Apply the distributive property.

$1 (- 3 - 2 i) + 8 i (- 3 - 2 i)$

Apply the distributive property.

$1 \cdot - 3 + 1 (- 2 i) + 8 i (- 3 - 2 i)$

Apply the distributive property.

$1 \cdot - 3 + 1 (- 2 i) + 8 i \cdot - 3 + 8 i (- 2 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 3$ by $1$ .

$- 3 + 1 (- 2 i) + 8 i \cdot - 3 + 8 i (- 2 i)$

Multiply $- 2 i$ by $1$ .

$- 3 - 2 i + 8 i \cdot - 3 + 8 i (- 2 i)$

Multiply $- 3$ by $8$ .

$- 3 - 2 i - 24 i + 8 i (- 2 i)$

Multiply $8 i (- 2 i)$ .

Multiply $- 2$ by $8$ .

$- 3 - 2 i - 24 i - 16 i i$

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

$- 3 - 2 i - 24 i - 16 (i^{1} i)$

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

$- 3 - 2 i - 24 i - 16 (i^{1} i^{1})$

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

$- 3 - 2 i - 24 i - 16 i^{1 + 1}$

Add $1$ and $1$ .

$- 3 - 2 i - 24 i - 16 i^{2}$

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

$- 3 - 2 i - 24 i - 16 \cdot - 1$

Multiply $- 16$ by $- 1$ .

$- 3 - 2 i - 24 i + 16$

Add $- 3$ and $16$ .

$13 - 2 i - 24 i$

Subtract $24 i$ from $- 2 i$ .

$13 - 26 i$