Simplify (3+4i)(3-4i)

$(3 + 4 i) (3 - 4 i)$

Step 1

Expand $(3 + 4 i) (3 - 4 i)$ using the FOIL Method.

Apply the distributive property.

$3 (3 - 4 i) + 4 i (3 - 4 i)$

Apply the distributive property.

$3 \cdot 3 + 3 (- 4 i) + 4 i (3 - 4 i)$

Apply the distributive property.

$3 \cdot 3 + 3 (- 4 i) + 4 i \cdot 3 + 4 i (- 4 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $3$ .

$9 + 3 (- 4 i) + 4 i \cdot 3 + 4 i (- 4 i)$

Multiply $- 4$ by $3$ .

$9 - 12 i + 4 i \cdot 3 + 4 i (- 4 i)$

Multiply $3$ by $4$ .

$9 - 12 i + 12 i + 4 i (- 4 i)$

Multiply $4 i (- 4 i)$ .

Multiply $- 4$ by $4$ .

$9 - 12 i + 12 i - 16 i i$

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

$9 - 12 i + 12 i - 16 (i^{1} i)$

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

$9 - 12 i + 12 i - 16 (i^{1} i^{1})$

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

$9 - 12 i + 12 i - 16 i^{1 + 1}$

Add $1$ and $1$ .

$9 - 12 i + 12 i - 16 i^{2}$

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

$9 - 12 i + 12 i - 16 \cdot - 1$

Multiply $- 16$ by $- 1$ .

$9 - 12 i + 12 i + 16$

Add $9$ and $16$ .

$25 - 12 i + 12 i$

Add $- 12 i$ and $12 i$ .

$25 + 0$

Add $25$ and $0$ .

$25$