Simplify (8+5i)(8-5i)

$(8 + 5 i) (8 - 5 i)$

Step 1

Expand $(8 + 5 i) (8 - 5 i)$ using the FOIL Method.

Apply the distributive property.

$8 (8 - 5 i) + 5 i (8 - 5 i)$

Apply the distributive property.

$8 \cdot 8 + 8 (- 5 i) + 5 i (8 - 5 i)$

Apply the distributive property.

$8 \cdot 8 + 8 (- 5 i) + 5 i \cdot 8 + 5 i (- 5 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $8$ .

$64 + 8 (- 5 i) + 5 i \cdot 8 + 5 i (- 5 i)$

Multiply $- 5$ by $8$ .

$64 - 40 i + 5 i \cdot 8 + 5 i (- 5 i)$

Multiply $8$ by $5$ .

$64 - 40 i + 40 i + 5 i (- 5 i)$

Multiply $5 i (- 5 i)$ .

Multiply $- 5$ by $5$ .

$64 - 40 i + 40 i - 25 i i$

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

$64 - 40 i + 40 i - 25 (i^{1} i)$

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

$64 - 40 i + 40 i - 25 (i^{1} i^{1})$

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

$64 - 40 i + 40 i - 25 i^{1 + 1}$

Add $1$ and $1$ .

$64 - 40 i + 40 i - 25 i^{2}$

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

$64 - 40 i + 40 i - 25 \cdot - 1$

Multiply $- 25$ by $- 1$ .

$64 - 40 i + 40 i + 25$

Add $64$ and $25$ .

$89 - 40 i + 40 i$

Add $- 40 i$ and $40 i$ .

$89 + 0$

Add $89$ and $0$ .

$89$