Simplify (3-9i)(3+9i)

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

Step 1

Expand $(3 - 9 i) (3 + 9 i)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $3$ .

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

Multiply $9$ by $3$ .

$9 + 27 i - 9 i \cdot 3 - 9 i (9 i)$

Multiply $3$ by $- 9$ .

$9 + 27 i - 27 i - 9 i (9 i)$

Multiply $- 9 i (9 i)$ .

Multiply $9$ by $- 9$ .

$9 + 27 i - 27 i - 81 i i$

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

$9 + 27 i - 27 i - 81 (i^{1} i)$

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

$9 + 27 i - 27 i - 81 (i^{1} i^{1})$

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

$9 + 27 i - 27 i - 81 i^{1 + 1}$

Add $1$ and $1$ .

$9 + 27 i - 27 i - 81 i^{2}$

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

$9 + 27 i - 27 i - 81 \cdot - 1$

Multiply $- 81$ by $- 1$ .

$9 + 27 i - 27 i + 81$

Add $9$ and $81$ .

$90 + 27 i - 27 i$

Subtract $27 i$ from $27 i$ .

$90 + 0$

Add $90$ and $0$ .

$90$