Simplify -i(4-8i)

$- i (4 - 8 i)$

Step 1

Apply the distributive property.

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

Step 2

Multiply $4$ by $- 1$ .

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

Step 3

Multiply $- i (- 8 i)$ .

Multiply $- 8$ by $- 1$ .

$- 4 i + 8 i i$

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

$- 4 i + 8 (i^{1} i)$

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

$- 4 i + 8 (i^{1} i^{1})$

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

$- 4 i + 8 i^{1 + 1}$

Add $1$ and $1$ .

$- 4 i + 8 i^{2}$

Step 4

Simplify each term.

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

$- 4 i + 8 \cdot - 1$

Multiply $8$ by $- 1$ .

$- 4 i - 8$

Step 5

Reorder $- 4 i$ and $- 8$ .

$- 8 - 4 i$