Simplify (5-6i)(6-2i)

$(5 - 6 i) (6 - 2 i)$

Step 1

Expand $(5 - 6 i) (6 - 2 i)$ using the FOIL Method.

Apply the distributive property.

$5 (6 - 2 i) - 6 i (6 - 2 i)$

Apply the distributive property.

$5 \cdot 6 + 5 (- 2 i) - 6 i (6 - 2 i)$

Apply the distributive property.

$5 \cdot 6 + 5 (- 2 i) - 6 i \cdot 6 - 6 i (- 2 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $6$ .

$30 + 5 (- 2 i) - 6 i \cdot 6 - 6 i (- 2 i)$

Multiply $- 2$ by $5$ .

$30 - 10 i - 6 i \cdot 6 - 6 i (- 2 i)$

Multiply $6$ by $- 6$ .

$30 - 10 i - 36 i - 6 i (- 2 i)$

Multiply $- 6 i (- 2 i)$ .

Multiply $- 2$ by $- 6$ .

$30 - 10 i - 36 i + 12 i i$

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

$30 - 10 i - 36 i + 12 (i^{1} i)$

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

$30 - 10 i - 36 i + 12 (i^{1} i^{1})$

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

$30 - 10 i - 36 i + 12 i^{1 + 1}$

Add $1$ and $1$ .

$30 - 10 i - 36 i + 12 i^{2}$

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

$30 - 10 i - 36 i + 12 \cdot - 1$

Multiply $12$ by $- 1$ .

$30 - 10 i - 36 i - 12$

Subtract $12$ from $30$ .

$18 - 10 i - 36 i$

Subtract $36 i$ from $- 10 i$ .

$18 - 46 i$