Simplify 8/(-4-2i)

$\frac{8}{- 4 - 2 i}$

Cancel the common factor of $8$ and $- 4 - 2 i$ .

Factor $2$ out of $8$ .

$\frac{2 (4)}{- 4 - 2 i}$

Cancel the common factors.

Factor $2$ out of $- 4$ .

$\frac{2 \cdot 4}{2 \cdot - 2 - 2 i}$

Factor $2$ out of $- 2 i$ .

$\frac{2 \cdot 4}{2 \cdot - 2 + 2 (- i)}$

Factor $2$ out of $2 (- 2) + 2 (- i)$ .

$\frac{2 \cdot 4}{2 (- 2 - i)}$

Cancel the common factor.

$\frac{2 \cdot 4}{2 (- 2 - i)}$

Rewrite the expression.

$\frac{4}{- 2 - i}$

Multiply the numerator and denominator of $\frac{4}{- 2 - i}$ by the conjugate of $- 2 - i$ to make the denominator real.

$\frac{4}{- 2 - i} \cdot \frac{- 2 + i}{- 2 + i}$

Multiply.

Combine.

$\frac{4 (- 2 + i)}{(- 2 - i) (- 2 + i)}$

Simplify the numerator.

Apply the distributive property.

$\frac{4 \cdot - 2 + 4 i}{(- 2 - i) (- 2 + i)}$

Multiply $4$ by $- 2$ .

$\frac{- 8 + 4 i}{(- 2 - i) (- 2 + i)}$

Simplify the denominator.

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

Apply the distributive property.

$\frac{- 8 + 4 i}{- 2 (- 2 + i) - i (- 2 + i)}$

Apply the distributive property.

$\frac{- 8 + 4 i}{- 2 \cdot - 2 - 2 i - i (- 2 + i)}$

Apply the distributive property.

$\frac{- 8 + 4 i}{- 2 \cdot - 2 - 2 i - i \cdot - 2 - i i}$

Simplify.

Multiply $- 2$ by $- 2$ .

$\frac{- 8 + 4 i}{4 - 2 i - i \cdot - 2 - i i}$

Multiply $- 2$ by $- 1$ .

$\frac{- 8 + 4 i}{4 - 2 i + 2 i - i i}$

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

$\frac{- 8 + 4 i}{4 - 2 i + 2 i - (i^{1} i)}$

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

$\frac{- 8 + 4 i}{4 - 2 i + 2 i - (i^{1} i^{1})}$

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

$\frac{- 8 + 4 i}{4 - 2 i + 2 i - i^{1 + 1}}$

Add $1$ and $1$ .

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

Add $- 2 i$ and $2 i$ .

$\frac{- 8 + 4 i}{4 + 0 - i^{2}}$

Add $4$ and $0$ .

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

Simplify each term.

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

$\frac{- 8 + 4 i}{4 - - 1}$

Multiply $- 1$ by $- 1$ .

$\frac{- 8 + 4 i}{4 + 1}$

Add $4$ and $1$ .

$\frac{- 8 + 4 i}{5}$

Split the fraction $\frac{- 8 + 4 i}{5}$ into two fractions.

$\frac{- 8}{5} + \frac{4 i}{5}$

Move the negative in front of the fraction.

$- \frac{8}{5} + \frac{4 i}{5}$

Simplify 8/(-4-2i)

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