Write in Standard Form (2+4i)(7-3i)

$(2 + 4 i) (7 - 3 i)$

Step 1

Expand $(2 + 4 i) (7 - 3 i)$ using the FOIL Method.

Apply the distributive property.

$2 (7 - 3 i) + 4 i (7 - 3 i)$

Apply the distributive property.

$2 \cdot 7 + 2 (- 3 i) + 4 i (7 - 3 i)$

Apply the distributive property.

$2 \cdot 7 + 2 (- 3 i) + 4 i \cdot 7 + 4 i (- 3 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $7$ .

$14 + 2 (- 3 i) + 4 i \cdot 7 + 4 i (- 3 i)$

Multiply $- 3$ by $2$ .

$14 - 6 i + 4 i \cdot 7 + 4 i (- 3 i)$

Multiply $7$ by $4$ .

$14 - 6 i + 28 i + 4 i (- 3 i)$

Multiply $4 i (- 3 i)$ .

Multiply $- 3$ by $4$ .

$14 - 6 i + 28 i - 12 i i$

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

$14 - 6 i + 28 i - 12 (i^{1} i)$

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

$14 - 6 i + 28 i - 12 (i^{1} i^{1})$

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

$14 - 6 i + 28 i - 12 i^{1 + 1}$

Add $1$ and $1$ .

$14 - 6 i + 28 i - 12 i^{2}$

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

$14 - 6 i + 28 i - 12 \cdot - 1$

Multiply $- 12$ by $- 1$ .

$14 - 6 i + 28 i + 12$

Add $14$ and $12$ .

$26 - 6 i + 28 i$

Add $- 6 i$ and $28 i$ .

$26 + 22 i$