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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $- 2$ by $4$ .

$- 8 - 2 (- 2 i) + 3 i \cdot 4 + 3 i (- 2 i)$

Multiply $- 2$ by $- 2$ .

$- 8 + 4 i + 3 i \cdot 4 + 3 i (- 2 i)$

Multiply $4$ by $3$ .

$- 8 + 4 i + 12 i + 3 i (- 2 i)$

Multiply $3 i (- 2 i)$ .

Multiply $- 2$ by $3$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply $- 6$ by $- 1$ .

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

Add $- 8$ and $6$ .

$- 2 + 4 i + 12 i$

Add $4 i$ and $12 i$ .

$- 2 + 16 i$