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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $- 4$ .

$- 20 + 5 (2 i) - 3 i \cdot - 4 - 3 i (2 i)$

Multiply $2$ by $5$ .

$- 20 + 10 i - 3 i \cdot - 4 - 3 i (2 i)$

Multiply $- 4$ by $- 3$ .

$- 20 + 10 i + 12 i - 3 i (2 i)$

Multiply $- 3 i (2 i)$ .

Multiply $2$ by $- 3$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply $- 6$ by $- 1$ .

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

Add $- 20$ and $6$ .

$- 14 + 10 i + 12 i$

Add $10 i$ and $12 i$ .

$- 14 + 22 i$