Simplify (3-5i)(4+6i)

$(3 - 5 i) (4 + 6 i)$

Step 1

Expand $(3 - 5 i) (4 + 6 i)$ using the FOIL Method.

Apply the distributive property.

$3 (4 + 6 i) - 5 i (4 + 6 i)$

Apply the distributive property.

$3 \cdot 4 + 3 (6 i) - 5 i (4 + 6 i)$

Apply the distributive property.

$3 \cdot 4 + 3 (6 i) - 5 i \cdot 4 - 5 i (6 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $4$ .

$12 + 3 (6 i) - 5 i \cdot 4 - 5 i (6 i)$

Multiply $6$ by $3$ .

$12 + 18 i - 5 i \cdot 4 - 5 i (6 i)$

Multiply $4$ by $- 5$ .

$12 + 18 i - 20 i - 5 i (6 i)$

Multiply $- 5 i (6 i)$ .

Multiply $6$ by $- 5$ .

$12 + 18 i - 20 i - 30 i i$

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

$12 + 18 i - 20 i - 30 (i^{1} i)$

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

$12 + 18 i - 20 i - 30 (i^{1} i^{1})$

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

$12 + 18 i - 20 i - 30 i^{1 + 1}$

Add $1$ and $1$ .

$12 + 18 i - 20 i - 30 i^{2}$

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

$12 + 18 i - 20 i - 30 \cdot - 1$

Multiply $- 30$ by $- 1$ .

$12 + 18 i - 20 i + 30$

Add $12$ and $30$ .

$42 + 18 i - 20 i$

Subtract $20 i$ from $18 i$ .

$42 - 2 i$