Simplify (2+8i)(2-8i)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

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

Multiply $- 8$ by $2$ .

$4 - 16 i + 8 i \cdot 2 + 8 i (- 8 i)$

Multiply $2$ by $8$ .

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

Multiply $8 i (- 8 i)$ .

Multiply $- 8$ by $8$ .

$4 - 16 i + 16 i - 64 i i$

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

$4 - 16 i + 16 i - 64 (i^{1} i)$

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

$4 - 16 i + 16 i - 64 (i^{1} i^{1})$

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

$4 - 16 i + 16 i - 64 i^{1 + 1}$

Add $1$ and $1$ .

$4 - 16 i + 16 i - 64 i^{2}$

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

$4 - 16 i + 16 i - 64 \cdot - 1$

Multiply $- 64$ by $- 1$ .

$4 - 16 i + 16 i + 64$

Add $4$ and $64$ .

$68 - 16 i + 16 i$

Add $- 16 i$ and $16 i$ .

$68 + 0$

Add $68$ and $0$ .

$68$