Simplify (7-6i)(2-3i)

$(7 - 6 i) (2 - 3 i)$

Step 1

Expand $(7 - 6 i) (2 - 3 i)$ using the FOIL Method.

Apply the distributive property.

$7 (2 - 3 i) - 6 i (2 - 3 i)$

Apply the distributive property.

$7 \cdot 2 + 7 (- 3 i) - 6 i (2 - 3 i)$

Apply the distributive property.

$7 \cdot 2 + 7 (- 3 i) - 6 i \cdot 2 - 6 i (- 3 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $7$ by $2$ .

$14 + 7 (- 3 i) - 6 i \cdot 2 - 6 i (- 3 i)$

Multiply $- 3$ by $7$ .

$14 - 21 i - 6 i \cdot 2 - 6 i (- 3 i)$

Multiply $2$ by $- 6$ .

$14 - 21 i - 12 i - 6 i (- 3 i)$

Multiply $- 6 i (- 3 i)$ .

Multiply $- 3$ by $- 6$ .

$14 - 21 i - 12 i + 18 i i$

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

$14 - 21 i - 12 i + 18 (i^{1} i)$

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

$14 - 21 i - 12 i + 18 (i^{1} i^{1})$

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

$14 - 21 i - 12 i + 18 i^{1 + 1}$

Add $1$ and $1$ .

$14 - 21 i - 12 i + 18 i^{2}$

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

$14 - 21 i - 12 i + 18 \cdot - 1$

Multiply $18$ by $- 1$ .

$14 - 21 i - 12 i - 18$

Subtract $18$ from $14$ .

$- 4 - 21 i - 12 i$

Subtract $12 i$ from $- 21 i$ .

$- 4 - 33 i$