Simplify (3-9i)^2

${(3 - 9 i)}^{2}$

Step 1

Rewrite ${(3 - 9 i)}^{2}$ as $(3 - 9 i) (3 - 9 i)$ .

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

Step 2

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 3

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 $- 1$ .

$9 - 27 i - 27 i - 81$

Subtract $81$ from $9$ .

$- 72 - 27 i - 27 i$

Subtract $27 i$ from $- 27 i$ .

$- 72 - 54 i$