Simplify (3i-2)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $3 i (3 i)$ .

Multiply $3$ by $3$ .

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

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

$9 (i^{1} i) + 3 i \cdot - 2 - 2 (3 i) - 2 \cdot - 2$

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

$9 (i^{1} i^{1}) + 3 i \cdot - 2 - 2 (3 i) - 2 \cdot - 2$

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

$9 i^{1 + 1} + 3 i \cdot - 2 - 2 (3 i) - 2 \cdot - 2$

Add $1$ and $1$ .

$9 i^{2} + 3 i \cdot - 2 - 2 (3 i) - 2 \cdot - 2$

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

$9 \cdot - 1 + 3 i \cdot - 2 - 2 (3 i) - 2 \cdot - 2$

Multiply $9$ by $- 1$ .

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

Multiply $- 2$ by $3$ .

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

Multiply $3$ by $- 2$ .

$- 9 - 6 i - 6 i - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

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

Add $- 9$ and $4$ .

$- 5 - 6 i - 6 i$

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

$- 5 - 12 i$