Evaluate (3-2i)^2

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

Step 1

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

$(3 - 2 i) (3 - 2 i)$

Step 2

Expand $(3 - 2 i) (3 - 2 i)$ using the FOIL Method.

Apply the distributive property.

$3 (3 - 2 i) - 2 i (3 - 2 i)$

Apply the distributive property.

$3 \cdot 3 + 3 (- 2 i) - 2 i (3 - 2 i)$

Apply the distributive property.

$3 \cdot 3 + 3 (- 2 i) - 2 i \cdot 3 - 2 i (- 2 i)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $3$ .

$9 + 3 (- 2 i) - 2 i \cdot 3 - 2 i (- 2 i)$

Multiply $- 2$ by $3$ .

$9 - 6 i - 2 i \cdot 3 - 2 i (- 2 i)$

Multiply $3$ by $- 2$ .

$9 - 6 i - 6 i - 2 i (- 2 i)$

Multiply $- 2 i (- 2 i)$ .

Multiply $- 2$ by $- 2$ .

$9 - 6 i - 6 i + 4 i i$

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

$9 - 6 i - 6 i + 4 (i^{1} i)$

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

$9 - 6 i - 6 i + 4 (i^{1} i^{1})$

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

$9 - 6 i - 6 i + 4 i^{1 + 1}$

Add $1$ and $1$ .

$9 - 6 i - 6 i + 4 i^{2}$

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

$9 - 6 i - 6 i + 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$9 - 6 i - 6 i - 4$

Subtract $4$ from $9$ .

$5 - 6 i - 6 i$

Subtract $6 i$ from $- 6 i$ .

$5 - 12 i$