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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $4$ .

$12 + 3 (- 3 i) + 2 i \cdot 4 + 2 i (- 3 i)$

Multiply $- 3$ by $3$ .

$12 - 9 i + 2 i \cdot 4 + 2 i (- 3 i)$

Multiply $4$ by $2$ .

$12 - 9 i + 8 i + 2 i (- 3 i)$

Multiply $2 i (- 3 i)$ .

Multiply $- 3$ by $2$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply $- 6$ by $- 1$ .

$12 - 9 i + 8 i + 6$

Add $12$ and $6$ .

$18 - 9 i + 8 i$

Add $- 9 i$ and $8 i$ .

$18 - i$