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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $- 4$ .

$- 12 + 3 (3 i) + i \cdot - 4 + i (3 i)$

Multiply $3$ by $3$ .

$- 12 + 9 i + i \cdot - 4 + i (3 i)$

Move $- 4$ to the left of $i$ .

$- 12 + 9 i - 4 \cdot i + i (3 i)$

Multiply $i (3 i)$ .

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

$- 12 + 9 i - 4 i + 3 (i^{1} i)$

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

$- 12 + 9 i - 4 i + 3 (i^{1} i^{1})$

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

$- 12 + 9 i - 4 i + 3 i^{1 + 1}$

Add $1$ and $1$ .

$- 12 + 9 i - 4 i + 3 i^{2}$

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

$- 12 + 9 i - 4 i + 3 \cdot - 1$

Multiply $3$ by $- 1$ .

$- 12 + 9 i - 4 i - 3$

Subtract $3$ from $- 12$ .

$- 15 + 9 i - 4 i$

Subtract $4 i$ from $9 i$ .

$- 15 + 5 i$