Simplify (4+8i)(4-8i)

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

Expand $(4 + 8 i) (4 - 8 i)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$16 + 4 (- 8 i) + 8 i \cdot 4 + 8 i (- 8 i)$

Multiply $- 8$ by $4$ .

$16 - 32 i + 8 i \cdot 4 + 8 i (- 8 i)$

Multiply $4$ by $8$ .

$16 - 32 i + 32 i + 8 i (- 8 i)$

Multiply $8 i (- 8 i)$ .

Multiply $- 8$ by $8$ .

$16 - 32 i + 32 i - 64 i i$

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

$16 - 32 i + 32 i - 64 (i^{1} i)$

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

$16 - 32 i + 32 i - 64 (i^{1} i^{1})$

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

$16 - 32 i + 32 i - 64 i^{1 + 1}$

Add $1$ and $1$ .

$16 - 32 i + 32 i - 64 i^{2}$

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

$16 - 32 i + 32 i - 64 \cdot - 1$

Multiply $- 64$ by $- 1$ .

$16 - 32 i + 32 i + 64$

Add $16$ and $64$ .

$80 - 32 i + 32 i$

Add $- 32 i$ and $32 i$ .

$80 + 0$

Add $80$ and $0$ .

$80$