Simplify (3-i)^2

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

Step 1

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

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

Step 2

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 3

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $3$ .

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

Multiply $- 1$ by $3$ .

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

Multiply $3$ by $- 1$ .

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

Multiply $- i (- i)$ .

Multiply $- 1$ by $- 1$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Multiply $i^{2}$ by $1$ .

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

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

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

$9 - 3 i - 3 i - 1$

$9 - 3 i - 3 i - 1$

Subtract $1$ from $9$ .

$8 - 3 i - 3 i$

Subtract $3 i$ from $- 3 i$ .

$8 - 6 i$

$8 - 6 i$

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