Simplify (6+7i)(6-7i)

$(6 + 7 i) (6 - 7 i)$

Step 1

Expand $(6 + 7 i) (6 - 7 i)$ using the FOIL Method.

Apply the distributive property.

$6 (6 - 7 i) + 7 i (6 - 7 i)$

Apply the distributive property.

$6 \cdot 6 + 6 (- 7 i) + 7 i (6 - 7 i)$

Apply the distributive property.

$6 \cdot 6 + 6 (- 7 i) + 7 i \cdot 6 + 7 i (- 7 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $6$ .

$36 + 6 (- 7 i) + 7 i \cdot 6 + 7 i (- 7 i)$

Multiply $- 7$ by $6$ .

$36 - 42 i + 7 i \cdot 6 + 7 i (- 7 i)$

Multiply $6$ by $7$ .

$36 - 42 i + 42 i + 7 i (- 7 i)$

Multiply $7 i (- 7 i)$ .

Multiply $- 7$ by $7$ .

$36 - 42 i + 42 i - 49 i i$

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

$36 - 42 i + 42 i - 49 (i^{1} i)$

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

$36 - 42 i + 42 i - 49 (i^{1} i^{1})$

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

$36 - 42 i + 42 i - 49 i^{1 + 1}$

Add $1$ and $1$ .

$36 - 42 i + 42 i - 49 i^{2}$

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

$36 - 42 i + 42 i - 49 \cdot - 1$

Multiply $- 49$ by $- 1$ .

$36 - 42 i + 42 i + 49$

Add $36$ and $49$ .

$85 - 42 i + 42 i$

Add $- 42 i$ and $42 i$ .

$85 + 0$

Add $85$ and $0$ .

$85$