Write in Standard Form (5+3i)(8-2i)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $8$ .

$40 + 5 (- 2 i) + 3 i \cdot 8 + 3 i (- 2 i)$

Multiply $- 2$ by $5$ .

$40 - 10 i + 3 i \cdot 8 + 3 i (- 2 i)$

Multiply $8$ by $3$ .

$40 - 10 i + 24 i + 3 i (- 2 i)$

Multiply $3 i (- 2 i)$ .

Multiply $- 2$ by $3$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply $- 6$ by $- 1$ .

$40 - 10 i + 24 i + 6$

Add $40$ and $6$ .

$46 - 10 i + 24 i$

Add $- 10 i$ and $24 i$ .

$46 + 14 i$