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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $- 2$ .

$- 6 + 3 (4 i) - 5 i \cdot - 2 - 5 i (4 i)$

Multiply $4$ by $3$ .

$- 6 + 12 i - 5 i \cdot - 2 - 5 i (4 i)$

Multiply $- 2$ by $- 5$ .

$- 6 + 12 i + 10 i - 5 i (4 i)$

Multiply $- 5 i (4 i)$ .

Multiply $4$ by $- 5$ .

$- 6 + 12 i + 10 i - 20 i i$

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

$- 6 + 12 i + 10 i - 20 (i^{1} i)$

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

$- 6 + 12 i + 10 i - 20 (i^{1} i^{1})$

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

$- 6 + 12 i + 10 i - 20 i^{1 + 1}$

Add $1$ and $1$ .

$- 6 + 12 i + 10 i - 20 i^{2}$

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

$- 6 + 12 i + 10 i - 20 \cdot - 1$

Multiply $- 20$ by $- 1$ .

$- 6 + 12 i + 10 i + 20$

Add $- 6$ and $20$ .

$14 + 12 i + 10 i$

Add $12 i$ and $10 i$ .

$14 + 22 i$