Simplify (1-3i)(1+3i)

$(1 - 3 i) (1 + 3 i)$

Step 1

Expand $(1 - 3 i) (1 + 3 i)$ using the FOIL Method.

Apply the distributive property.

$1 (1 + 3 i) - 3 i (1 + 3 i)$

Apply the distributive property.

$1 \cdot 1 + 1 (3 i) - 3 i (1 + 3 i)$

Apply the distributive property.

$1 \cdot 1 + 1 (3 i) - 3 i \cdot 1 - 3 i (3 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $1$ by $1$ .

$1 + 1 (3 i) - 3 i \cdot 1 - 3 i (3 i)$

Multiply $3 i$ by $1$ .

$1 + 3 i - 3 i \cdot 1 - 3 i (3 i)$

Multiply $- 3$ by $1$ .

$1 + 3 i - 3 i - 3 i (3 i)$

Multiply $- 3 i (3 i)$ .

Multiply $3$ by $- 3$ .

$1 + 3 i - 3 i - 9 i i$

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

$1 + 3 i - 3 i - 9 (i^{1} i)$

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

$1 + 3 i - 3 i - 9 (i^{1} i^{1})$

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

$1 + 3 i - 3 i - 9 i^{1 + 1}$

Add $1$ and $1$ .

$1 + 3 i - 3 i - 9 i^{2}$

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

$1 + 3 i - 3 i - 9 \cdot - 1$

Multiply $- 9$ by $- 1$ .

$1 + 3 i - 3 i + 9$

Add $1$ and $9$ .

$10 + 3 i - 3 i$

Subtract $3 i$ from $3 i$ .

$10 + 0$

Add $10$ and $0$ .

$10$