Simplify (7-3i)(7+3i)

$(7 - 3 i) (7 + 3 i)$

Step 1

Expand $(7 - 3 i) (7 + 3 i)$ using the FOIL Method.

Apply the distributive property.

$7 (7 + 3 i) - 3 i (7 + 3 i)$

Apply the distributive property.

$7 \cdot 7 + 7 (3 i) - 3 i (7 + 3 i)$

Apply the distributive property.

$7 \cdot 7 + 7 (3 i) - 3 i \cdot 7 - 3 i (3 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $7$ by $7$ .

$49 + 7 (3 i) - 3 i \cdot 7 - 3 i (3 i)$

Multiply $3$ by $7$ .

$49 + 21 i - 3 i \cdot 7 - 3 i (3 i)$

Multiply $7$ by $- 3$ .

$49 + 21 i - 21 i - 3 i (3 i)$

Multiply $- 3 i (3 i)$ .

Multiply $3$ by $- 3$ .

$49 + 21 i - 21 i - 9 i i$

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

$49 + 21 i - 21 i - 9 (i^{1} i)$

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

$49 + 21 i - 21 i - 9 (i^{1} i^{1})$

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

$49 + 21 i - 21 i - 9 i^{1 + 1}$

Add $1$ and $1$ .

$49 + 21 i - 21 i - 9 i^{2}$

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

$49 + 21 i - 21 i - 9 \cdot - 1$

Multiply $- 9$ by $- 1$ .

$49 + 21 i - 21 i + 9$

Add $49$ and $9$ .

$58 + 21 i - 21 i$

Subtract $21 i$ from $21 i$ .

$58 + 0$

Add $58$ and $0$ .

$58$