Simplify -3+6i-4i(-5-2i)+8i^3

$- 3 + 6 i - 4 i (- 5 - 2 i) + 8 i^{3}$

Step 1

Simplify each term.

Apply the distributive property.

$- 3 + 6 i - 4 i \cdot - 5 - 4 i (- 2 i) + 8 i^{3}$

Multiply $- 5$ by $- 4$ .

$- 3 + 6 i + 20 i - 4 i (- 2 i) + 8 i^{3}$

Multiply $- 4 i (- 2 i)$ .

Multiply $- 2$ by $- 4$ .

$- 3 + 6 i + 20 i + 8 i i + 8 i^{3}$

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

$- 3 + 6 i + 20 i + 8 (i^{1} i) + 8 i^{3}$

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

$- 3 + 6 i + 20 i + 8 (i^{1} i^{1}) + 8 i^{3}$

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

$- 3 + 6 i + 20 i + 8 i^{1 + 1} + 8 i^{3}$

Add $1$ and $1$ .

$- 3 + 6 i + 20 i + 8 i^{2} + 8 i^{3}$

Simplify each term.

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

$- 3 + 6 i + 20 i + 8 \cdot - 1 + 8 i^{3}$

Multiply $8$ by $- 1$ .

$- 3 + 6 i + 20 i - 8 + 8 i^{3}$

Factor out $i^{2}$ .

$- 3 + 6 i + 20 i - 8 + 8 (i^{2} \cdot i)$

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

$- 3 + 6 i + 20 i - 8 + 8 (- 1 \cdot i)$

Rewrite $- 1 i$ as $- i$ .

$- 3 + 6 i + 20 i - 8 + 8 (- i)$

Multiply $- 1$ by $8$ .

$- 3 + 6 i + 20 i - 8 - 8 i$

Step 2

Simplify by adding terms.

Subtract $8$ from $- 3$ .

$- 11 + 6 i + 20 i - 8 i$

Add $6 i$ and $20 i$ .

$- 11 + 26 i - 8 i$

Subtract $8 i$ from $26 i$ .

$- 11 + 18 i$