Simplify (6-2i)(2-3i)

$(6 - 2 i) (2 - 3 i)$

Step 1

Expand $(6 - 2 i) (2 - 3 i)$ using the FOIL Method.

Apply the distributive property.

$6 (2 - 3 i) - 2 i (2 - 3 i)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $2$ .

$12 + 6 (- 3 i) - 2 i \cdot 2 - 2 i (- 3 i)$

Multiply $- 3$ by $6$ .

$12 - 18 i - 2 i \cdot 2 - 2 i (- 3 i)$

Multiply $2$ by $- 2$ .

$12 - 18 i - 4 i - 2 i (- 3 i)$

Multiply $- 2 i (- 3 i)$ .

Multiply $- 3$ by $- 2$ .

$12 - 18 i - 4 i + 6 i i$

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

$12 - 18 i - 4 i + 6 (i^{1} i)$

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

$12 - 18 i - 4 i + 6 (i^{1} i^{1})$

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

$12 - 18 i - 4 i + 6 i^{1 + 1}$

Add $1$ and $1$ .

$12 - 18 i - 4 i + 6 i^{2}$

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

$12 - 18 i - 4 i + 6 \cdot - 1$

Multiply $6$ by $- 1$ .

$12 - 18 i - 4 i - 6$

Subtract $6$ from $12$ .

$6 - 18 i - 4 i$

Subtract $4 i$ from $- 18 i$ .

$6 - 22 i$