Simplify (5+7i)(5-7i)

$(5 + 7 i) (5 - 7 i)$

Step 1

Expand $(5 + 7 i) (5 - 7 i)$ using the FOIL Method.

Apply the distributive property.

$5 (5 - 7 i) + 7 i (5 - 7 i)$

Apply the distributive property.

$5 \cdot 5 + 5 (- 7 i) + 7 i (5 - 7 i)$

Apply the distributive property.

$5 \cdot 5 + 5 (- 7 i) + 7 i \cdot 5 + 7 i (- 7 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $5$ .

$25 + 5 (- 7 i) + 7 i \cdot 5 + 7 i (- 7 i)$

Multiply $- 7$ by $5$ .

$25 - 35 i + 7 i \cdot 5 + 7 i (- 7 i)$

Multiply $5$ by $7$ .

$25 - 35 i + 35 i + 7 i (- 7 i)$

Multiply $7 i (- 7 i)$ .

Multiply $- 7$ by $7$ .

$25 - 35 i + 35 i - 49 i i$

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

$25 - 35 i + 35 i - 49 (i^{1} i)$

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

$25 - 35 i + 35 i - 49 (i^{1} i^{1})$

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

$25 - 35 i + 35 i - 49 i^{1 + 1}$

Add $1$ and $1$ .

$25 - 35 i + 35 i - 49 i^{2}$

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

$25 - 35 i + 35 i - 49 \cdot - 1$

Multiply $- 49$ by $- 1$ .

$25 - 35 i + 35 i + 49$

Add $25$ and $49$ .

$74 - 35 i + 35 i$

Add $- 35 i$ and $35 i$ .

$74 + 0$

Add $74$ and $0$ .

$74$