Simplify (9-3i)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $9$ by $9$ .

$81 + 9 (- 3 i) - 3 i \cdot 9 - 3 i (- 3 i)$

Multiply $- 3$ by $9$ .

$81 - 27 i - 3 i \cdot 9 - 3 i (- 3 i)$

Multiply $9$ by $- 3$ .

$81 - 27 i - 27 i - 3 i (- 3 i)$

Multiply $- 3 i (- 3 i)$ .

Multiply $- 3$ by $- 3$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply $9$ by $- 1$ .

$81 - 27 i - 27 i - 9$

Subtract $9$ from $81$ .

$72 - 27 i - 27 i$

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

$72 - 54 i$