Simplify (8i)/(-4-4i)

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

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

Factor $4$ out of $8 i$ .

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

Cancel the common factors.

Factor $4$ out of $- 4$ .

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

Factor $4$ out of $- 4 i$ .

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

Factor $4$ out of $4 (- 1) + 4 (- i)$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2 i}{- 1 - i}$

Multiply the numerator and denominator of $\frac{2 i}{- 1 - i}$ by the conjugate of $- 1 - i$ to make the denominator real.

$\frac{2 i}{- 1 - i} \cdot \frac{- 1 + i}{- 1 + i}$

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

$\frac{2 i \cdot - 1 + 2 i i}{(- 1 - i) (- 1 + i)}$

Multiply $- 1$ by $2$ .

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

Multiply $2 i i$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

Simplify each term.

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

$\frac{- 2 i + 2 \cdot - 1}{(- 1 - i) (- 1 + i)}$

Multiply $2$ by $- 1$ .

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

Reorder $- 2 i$ and $- 2$ .

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

Simplify the denominator.

Expand $(- 1 - i) (- 1 + i)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

$\frac{- 2 - 2 i}{- 1 \cdot - 1 - 1 i - i (- 1 + i)}$

Apply the distributive property.

$\frac{- 2 - 2 i}{- 1 \cdot - 1 - 1 i - i \cdot - 1 - i i}$

Simplify.

Multiply $- 1$ by $- 1$ .

$\frac{- 2 - 2 i}{1 - 1 i - i \cdot - 1 - i i}$

Multiply $- 1$ by $- 1$ .

$\frac{- 2 - 2 i}{1 - 1 i + 1 i - i i}$

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

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

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

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

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

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

Add $1$ and $1$ .

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

Add $- 1 i$ and $1 i$ .

$\frac{- 2 - 2 i}{1 + 0 - i^{2}}$

Add $1$ and $0$ .

$\frac{- 2 - 2 i}{1 - i^{2}}$

Simplify each term.

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

$\frac{- 2 - 2 i}{1 - - 1}$

Multiply $- 1$ by $- 1$ .

$\frac{- 2 - 2 i}{1 + 1}$

Add $1$ and $1$ .

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

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

Factor $2$ out of $- 2$ .

$\frac{2 \cdot - 1 - 2 i}{2}$

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

$\frac{2 \cdot - 1 + 2 (- i)}{2}$

Factor $2$ out of $2 (- 1) + 2 (- i)$ .

$\frac{2 (- 1 - i)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{2 (- 1 - i)}{2 (1)}$

Cancel the common factor.

$\frac{2 (- 1 - i)}{2 \cdot 1}$

Rewrite the expression.

$\frac{- 1 - i}{1}$

Divide $- 1 - i$ by $1$ .

$- 1 - i$

Simplify (8i)/(-4-4i)

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