Simplify (3-5i)(8-2i)

$(3 - 5 i) (8 - 2 i)$

Step 1

Expand $(3 - 5 i) (8 - 2 i)$ using the FOIL Method.

Apply the distributive property.

$3 (8 - 2 i) - 5 i (8 - 2 i)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $8$ .

$24 + 3 (- 2 i) - 5 i \cdot 8 - 5 i (- 2 i)$

Multiply $- 2$ by $3$ .

$24 - 6 i - 5 i \cdot 8 - 5 i (- 2 i)$

Multiply $8$ by $- 5$ .

$24 - 6 i - 40 i - 5 i (- 2 i)$

Multiply $- 5 i (- 2 i)$ .

Multiply $- 2$ by $- 5$ .

$24 - 6 i - 40 i + 10 i i$

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

$24 - 6 i - 40 i + 10 (i^{1} i)$

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

$24 - 6 i - 40 i + 10 (i^{1} i^{1})$

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

$24 - 6 i - 40 i + 10 i^{1 + 1}$

Add $1$ and $1$ .

$24 - 6 i - 40 i + 10 i^{2}$

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

$24 - 6 i - 40 i + 10 \cdot - 1$

Multiply $10$ by $- 1$ .

$24 - 6 i - 40 i - 10$

Subtract $10$ from $24$ .

$14 - 6 i - 40 i$

Subtract $40 i$ from $- 6 i$ .

$14 - 46 i$