Find the Product (-3+2j)(4j-7)

$(- 3 + 2 j) (4 j - 7)$

Step 1

Expand $(- 3 + 2 j) (4 j - 7)$ using the FOIL Method.

Apply the distributive property.

$- 3 (4 j - 7) + 2 j (4 j - 7)$

Apply the distributive property.

$- 3 (4 j) - 3 \cdot - 7 + 2 j (4 j - 7)$

Apply the distributive property.

$- 3 (4 j) - 3 \cdot - 7 + 2 j (4 j) + 2 j \cdot - 7$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $- 3$ .

$- 12 j - 3 \cdot - 7 + 2 j (4 j) + 2 j \cdot - 7$

Multiply $- 3$ by $- 7$ .

$- 12 j + 21 + 2 j (4 j) + 2 j \cdot - 7$

Rewrite using the commutative property of multiplication.

$- 12 j + 21 + 2 \cdot 4 j \cdot j + 2 j \cdot - 7$

Multiply $j$ by $j$ by adding the exponents.

Move $j$ .

$- 12 j + 21 + 2 \cdot 4 (j \cdot j) + 2 j \cdot - 7$

Multiply $j$ by $j$ .

$- 12 j + 21 + 2 \cdot 4 j^{2} + 2 j \cdot - 7$

Multiply $2$ by $4$ .

$- 12 j + 21 + 8 j^{2} + 2 j \cdot - 7$

Multiply $- 7$ by $2$ .

$- 12 j + 21 + 8 j^{2} - 14 j$

Subtract $14 j$ from $- 12 j$ .

$- 26 j + 21 + 8 j^{2}$