Simplify (4-5i)(3+2i)

$(4 - 5 i) (3 + 2 i)$

Step 1

Expand $(4 - 5 i) (3 + 2 i)$ using the FOIL Method.

Apply the distributive property.

$4 (3 + 2 i) - 5 i (3 + 2 i)$

Apply the distributive property.

$4 \cdot 3 + 4 (2 i) - 5 i (3 + 2 i)$

Apply the distributive property.

$4 \cdot 3 + 4 (2 i) - 5 i \cdot 3 - 5 i (2 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $3$ .

$12 + 4 (2 i) - 5 i \cdot 3 - 5 i (2 i)$

Multiply $2$ by $4$ .

$12 + 8 i - 5 i \cdot 3 - 5 i (2 i)$

Multiply $3$ by $- 5$ .

$12 + 8 i - 15 i - 5 i (2 i)$

Multiply $- 5 i (2 i)$ .

Multiply $2$ by $- 5$ .

$12 + 8 i - 15 i - 10 i i$

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

$12 + 8 i - 15 i - 10 (i^{1} i)$

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

$12 + 8 i - 15 i - 10 (i^{1} i^{1})$

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

$12 + 8 i - 15 i - 10 i^{1 + 1}$

Add $1$ and $1$ .

$12 + 8 i - 15 i - 10 i^{2}$

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

$12 + 8 i - 15 i - 10 \cdot - 1$

Multiply $- 10$ by $- 1$ .

$12 + 8 i - 15 i + 10$

Add $12$ and $10$ .

$22 + 8 i - 15 i$

Subtract $15 i$ from $8 i$ .

$22 - 7 i$