Simplify (3+i)(3-i)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $3$ .

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

Multiply $- 1$ by $3$ .

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

Move $3$ to the left of $i$ .

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

Multiply $i (- i)$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

Multiply $- 1$ by $- 1$ .

$9 - 3 i + 3 i + 1$

$9 - 3 i + 3 i + 1$

Add $9$ and $1$ .

$10 - 3 i + 3 i$

Add $- 3 i$ and $3 i$ .

$10 + 0$

Add $10$ and $0$ .

$10$

$10$

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