Simplify (6-4i)(6+4i)

$(6 - 4 i) (6 + 4 i)$

Step 1

Expand $(6 - 4 i) (6 + 4 i)$ using the FOIL Method.

Apply the distributive property.

$6 (6 + 4 i) - 4 i (6 + 4 i)$

Apply the distributive property.

$6 \cdot 6 + 6 (4 i) - 4 i (6 + 4 i)$

Apply the distributive property.

$6 \cdot 6 + 6 (4 i) - 4 i \cdot 6 - 4 i (4 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $6$ .

$36 + 6 (4 i) - 4 i \cdot 6 - 4 i (4 i)$

Multiply $4$ by $6$ .

$36 + 24 i - 4 i \cdot 6 - 4 i (4 i)$

Multiply $6$ by $- 4$ .

$36 + 24 i - 24 i - 4 i (4 i)$

Multiply $- 4 i (4 i)$ .

Multiply $4$ by $- 4$ .

$36 + 24 i - 24 i - 16 i i$

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

$36 + 24 i - 24 i - 16 (i^{1} i)$

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

$36 + 24 i - 24 i - 16 (i^{1} i^{1})$

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

$36 + 24 i - 24 i - 16 i^{1 + 1}$

Add $1$ and $1$ .

$36 + 24 i - 24 i - 16 i^{2}$

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

$36 + 24 i - 24 i - 16 \cdot - 1$

Multiply $- 16$ by $- 1$ .

$36 + 24 i - 24 i + 16$

Add $36$ and $16$ .

$52 + 24 i - 24 i$

Subtract $24 i$ from $24 i$ .

$52 + 0$

Add $52$ and $0$ .

$52$