Simplify (8-4i)(-3+9i)

$(8 - 4 i) (- 3 + 9 i)$

Step 1

Expand $(8 - 4 i) (- 3 + 9 i)$ using the FOIL Method.

Apply the distributive property.

$8 (- 3 + 9 i) - 4 i (- 3 + 9 i)$

Apply the distributive property.

$8 \cdot - 3 + 8 (9 i) - 4 i (- 3 + 9 i)$

Apply the distributive property.

$8 \cdot - 3 + 8 (9 i) - 4 i \cdot - 3 - 4 i (9 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $- 3$ .

$- 24 + 8 (9 i) - 4 i \cdot - 3 - 4 i (9 i)$

Multiply $9$ by $8$ .

$- 24 + 72 i - 4 i \cdot - 3 - 4 i (9 i)$

Multiply $- 3$ by $- 4$ .

$- 24 + 72 i + 12 i - 4 i (9 i)$

Multiply $- 4 i (9 i)$ .

Multiply $9$ by $- 4$ .

$- 24 + 72 i + 12 i - 36 i i$

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

$- 24 + 72 i + 12 i - 36 (i^{1} i)$

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

$- 24 + 72 i + 12 i - 36 (i^{1} i^{1})$

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

$- 24 + 72 i + 12 i - 36 i^{1 + 1}$

Add $1$ and $1$ .

$- 24 + 72 i + 12 i - 36 i^{2}$

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

$- 24 + 72 i + 12 i - 36 \cdot - 1$

Multiply $- 36$ by $- 1$ .

$- 24 + 72 i + 12 i + 36$

Add $- 24$ and $36$ .

$12 + 72 i + 12 i$

Add $72 i$ and $12 i$ .

$12 + 84 i$