Algebra Examples

$(- 3 + 2 i) (- 6 - 8 i)$

Step 1

Expand $(- 3 + 2 i) (- 6 - 8 i)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$- 3 (- 6 - 8 i) + 2 i (- 6 - 8 i)$

Step 1.2

Apply the distributive property.

$- 3 \cdot - 6 - 3 (- 8 i) + 2 i (- 6 - 8 i)$

Step 1.3

Apply the distributive property.

$- 3 \cdot - 6 - 3 (- 8 i) + 2 i \cdot - 6 + 2 i (- 8 i)$

Step 2

Simplify and combine like terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Multiply $- 3$ by $- 6$ .

$18 - 3 (- 8 i) + 2 i \cdot - 6 + 2 i (- 8 i)$

Step 2.1.2

Multiply $- 8$ by $- 3$ .

$18 + 24 i + 2 i \cdot - 6 + 2 i (- 8 i)$

Step 2.1.3

Multiply $- 6$ by $2$ .

$18 + 24 i - 12 i + 2 i (- 8 i)$

Step 2.1.4

Multiply $2 i (- 8 i)$ .

Tap for more steps...

Step 2.1.4.1

Multiply $- 8$ by $2$ .

$18 + 24 i - 12 i - 16 i i$

Step 2.1.4.2

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

$18 + 24 i - 12 i - 16 (i^{1} i)$

Step 2.1.4.3

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

$18 + 24 i - 12 i - 16 (i^{1} i^{1})$

Step 2.1.4.4

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

$18 + 24 i - 12 i - 16 i^{1 + 1}$

Step 2.1.4.5

Add $1$ and $1$ .

$18 + 24 i - 12 i - 16 i^{2}$

Step 2.1.5

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

$18 + 24 i - 12 i - 16 \cdot - 1$

Step 2.1.6

Multiply $- 16$ by $- 1$ .

$18 + 24 i - 12 i + 16$

Step 2.2

Add $18$ and $16$ .

$34 + 24 i - 12 i$

Step 2.3

Subtract $12 i$ from $24 i$ .

$34 + 12 i$