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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

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

Multiply $- 4$ by $2$ .

$4 - 8 i + 4 i \cdot 2 + 4 i (- 4 i)$

Multiply $2$ by $4$ .

$4 - 8 i + 8 i + 4 i (- 4 i)$

Multiply $4 i (- 4 i)$ .

Multiply $- 4$ by $4$ .

$4 - 8 i + 8 i - 16 i i$

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

$4 - 8 i + 8 i - 16 (i^{1} i)$

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

$4 - 8 i + 8 i - 16 (i^{1} i^{1})$

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

$4 - 8 i + 8 i - 16 i^{1 + 1}$

Add $1$ and $1$ .

$4 - 8 i + 8 i - 16 i^{2}$

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

$4 - 8 i + 8 i - 16 \cdot - 1$

Multiply $- 16$ by $- 1$ .

$4 - 8 i + 8 i + 16$

Add $4$ and $16$ .

$20 - 8 i + 8 i$

Add $- 8 i$ and $8 i$ .

$20 + 0$

Add $20$ and $0$ .

$20$