Simplify (4-6i)(6-8i)

$(4 - 6 i) (6 - 8 i)$

Step 1

Expand $(4 - 6 i) (6 - 8 i)$ using the FOIL Method.

Apply the distributive property.

$4 (6 - 8 i) - 6 i (6 - 8 i)$

Apply the distributive property.

$4 \cdot 6 + 4 (- 8 i) - 6 i (6 - 8 i)$

Apply the distributive property.

$4 \cdot 6 + 4 (- 8 i) - 6 i \cdot 6 - 6 i (- 8 i)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $6$ .

$24 + 4 (- 8 i) - 6 i \cdot 6 - 6 i (- 8 i)$

Multiply $- 8$ by $4$ .

$24 - 32 i - 6 i \cdot 6 - 6 i (- 8 i)$

Multiply $6$ by $- 6$ .

$24 - 32 i - 36 i - 6 i (- 8 i)$

Multiply $- 6 i (- 8 i)$ .

Multiply $- 8$ by $- 6$ .

$24 - 32 i - 36 i + 48 i i$

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

$24 - 32 i - 36 i + 48 (i^{1} i)$

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

$24 - 32 i - 36 i + 48 (i^{1} i^{1})$

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

$24 - 32 i - 36 i + 48 i^{1 + 1}$

Add $1$ and $1$ .

$24 - 32 i - 36 i + 48 i^{2}$

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

$24 - 32 i - 36 i + 48 \cdot - 1$

Multiply $48$ by $- 1$ .

$24 - 32 i - 36 i - 48$

Subtract $48$ from $24$ .

$- 24 - 32 i - 36 i$

Subtract $36 i$ from $- 32 i$ .

$- 24 - 68 i$