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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $- 2$ .

$- 6 + 3 (4 i) + 2 i \cdot - 2 + 2 i (4 i)$

Multiply $4$ by $3$ .

$- 6 + 12 i + 2 i \cdot - 2 + 2 i (4 i)$

Multiply $- 2$ by $2$ .

$- 6 + 12 i - 4 i + 2 i (4 i)$

Multiply $2 i (4 i)$ .

Multiply $4$ by $2$ .

$- 6 + 12 i - 4 i + 8 i i$

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

$- 6 + 12 i - 4 i + 8 (i^{1} i)$

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

$- 6 + 12 i - 4 i + 8 (i^{1} i^{1})$

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

$- 6 + 12 i - 4 i + 8 i^{1 + 1}$

Add $1$ and $1$ .

$- 6 + 12 i - 4 i + 8 i^{2}$

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

$- 6 + 12 i - 4 i + 8 \cdot - 1$

Multiply $8$ by $- 1$ .

$- 6 + 12 i - 4 i - 8$

Subtract $8$ from $- 6$ .

$- 14 + 12 i - 4 i$

Subtract $4 i$ from $12 i$ .

$- 14 + 8 i$