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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $3$ .

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

Multiply $4$ by $2$ .

$6 + 8 i - 3 i \cdot 3 - 3 i (4 i)$

Multiply $3$ by $- 3$ .

$6 + 8 i - 9 i - 3 i (4 i)$

Multiply $- 3 i (4 i)$ .

Multiply $4$ by $- 3$ .

$6 + 8 i - 9 i - 12 i i$

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

$6 + 8 i - 9 i - 12 (i^{1} i)$

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

$6 + 8 i - 9 i - 12 (i^{1} i^{1})$

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

$6 + 8 i - 9 i - 12 i^{1 + 1}$

Add $1$ and $1$ .

$6 + 8 i - 9 i - 12 i^{2}$

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

$6 + 8 i - 9 i - 12 \cdot - 1$

Multiply $- 12$ by $- 1$ .

$6 + 8 i - 9 i + 12$

Add $6$ and $12$ .

$18 + 8 i - 9 i$

Subtract $9 i$ from $8 i$ .

$18 - i$