Simplify (8+7i)(8-7i)

$(8 + 7 i) (8 - 7 i)$

Step 1

Expand $(8 + 7 i) (8 - 7 i)$ using the FOIL Method.

Apply the distributive property.

$8 (8 - 7 i) + 7 i (8 - 7 i)$

Apply the distributive property.

$8 \cdot 8 + 8 (- 7 i) + 7 i (8 - 7 i)$

Apply the distributive property.

$8 \cdot 8 + 8 (- 7 i) + 7 i \cdot 8 + 7 i (- 7 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $8$ .

$64 + 8 (- 7 i) + 7 i \cdot 8 + 7 i (- 7 i)$

Multiply $- 7$ by $8$ .

$64 - 56 i + 7 i \cdot 8 + 7 i (- 7 i)$

Multiply $8$ by $7$ .

$64 - 56 i + 56 i + 7 i (- 7 i)$

Multiply $7 i (- 7 i)$ .

Multiply $- 7$ by $7$ .

$64 - 56 i + 56 i - 49 i i$

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

$64 - 56 i + 56 i - 49 (i^{1} i)$

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

$64 - 56 i + 56 i - 49 (i^{1} i^{1})$

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

$64 - 56 i + 56 i - 49 i^{1 + 1}$

Add $1$ and $1$ .

$64 - 56 i + 56 i - 49 i^{2}$

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

$64 - 56 i + 56 i - 49 \cdot - 1$

Multiply $- 49$ by $- 1$ .

$64 - 56 i + 56 i + 49$

Add $64$ and $49$ .

$113 - 56 i + 56 i$

Add $- 56 i$ and $56 i$ .

$113 + 0$

Add $113$ and $0$ .

$113$