Evaluate 4i(-2-8i)

$4 i (- 2 - 8 i)$

Step 1

Apply the distributive property.

$4 i \cdot - 2 + 4 i (- 8 i)$

Step 2

Multiply $- 2$ by $4$ .

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

Step 3

Multiply $4 i (- 8 i)$ .

Multiply $- 8$ by $4$ .

$- 8 i - 32 i i$

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

$- 8 i - 32 (i^{1} i)$

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

$- 8 i - 32 (i^{1} i^{1})$

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

$- 8 i - 32 i^{1 + 1}$

Add $1$ and $1$ .

$- 8 i - 32 i^{2}$

Step 4

Simplify each term.

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

$- 8 i - 32 \cdot - 1$

Multiply $- 32$ by $- 1$ .

$- 8 i + 32$

Step 5

Reorder $- 8 i$ and $32$ .

$32 - 8 i$